Product Calculus Answers and News

Product Calculus Questions and Answers

Open Question: Question in macroeconomics.I tried answering.?

2.(This problem requires the use of calculus.) Con- sider a Cobb–Douglas production function with three inputs. Kis capital (the number of ma- chines),Lis labor (the number of workers),and H is human capital (the number of college degrees among the workers).The production function is Y=K1/3L1/3H1/3. a. Derive an expression for the marginal product of labor.How does an increase in the amount of human capital affect the marginal product of labor? b. Derive an expression for the marginal product of human capital.How does an increase in the amount of human capital affect the marginal product of human capital? c. What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income do you think workers would appear to receive? (Hint: Consider where the return to human capital shows up.) d. An unskilled worker earns the marginal prod- uct of labor,whereas a skilled worker earns the marginal product of labor plus the marginal product of human capital.Using your answers to (a) and (b),ﬁnd the ratio of the skilled wage to the unskilled wage.How does an increase in the amount of human capital affect this ratio? Explain. e. Some people advocate government funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholar- ships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate? more

Resolved Question: Is this calculus correct?

f(x)=1/(x+1)= (x+1)^-1 f '(x)= -1(x+1)^-2 or -1/(x+1)^2 Did I do this correctly? If so, could I do f '(x) if f(x)=(x^2 +3)/(x+1) as (x^2 +3) (x+1)^-1 and just use the product rule? I want to avoid using the quotient rule. Oddly it almost looks like I am using the composite function rule and the product rule to get the quotient rule. Could someone clarify for me please? Thanks, I didnt realize I was just using the quotient rule haha. Well atleast I discovered for myself how it was found. more

Open Question: Calc Help!!!!!!!!!!!!!?

The ordering and transportation cost for the components used in manufacturing a certain product is C=100((200/(x^2))+(x/(x+30))), 1<=x where C is the cost (in thousands of dollars) and x is the order size (in hundreds). In calculus, it can be shown that the cost is a minimum when 3x^3 - 40x^2 - 2400x - 36000=0. Using a calculator, estimate the optimal order size to the nearest hundred units. What should I do? Please take me step by step more

Resolved Question: Please help me with calculus!!!?

7.) Find the third derivative of f(x) = 4x^5 + 6x^3 + 2x + 1, with respect to x. 240x + 36 240 240x^2 + 36 x^2 + 36 8.) Find all points of inflection that occur on the function y = x^3 + 4x. x = 0 x = 0, 1 x = -1, 1 x = 2 9.) A baseball is hit into the air and has position function s(t) = -16t^2 + 25t + 4. Find the velocity. -32t + 25 -32t 32t - 25 -t + 25 10.) Find the acceleration of the baseball in #9. 32 109 -32 22 11.) The weight in kilograms of rocket fuel in a rocket launcher is given by W = (1/t) - (4/t^2), where t is time in seconds. At time t = 10 seconds, the amount of fuel in the launcher is decreasing at a rate of _____ kilograms per second. 0.01 0.002 1.343 1.701 12.) Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. When the diameter of the balloon is 20 cm, the radius of the balloon is increasing at a rate of ____ cm per minute. 1/80 80pi 1/80pi -1/80pi 13.) Find two nonnegative numbers whose sum is 9, such that the product of one number and the square of the other number is a maximum. 3, 6 3, 9 2, 6 2, 2 14.) There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees? 16 6 50 15 15.) Differentiate: sin(x) dx = cos(x) + C -cos(x) + C sin(x) + C 1/sin(x) + C more

Voting Question: Please help me with calculus!!! 10 pts for best answer?

1.) Is f(x) = (x^2 - 9) / (x - 3) a continuous function? No Yes Not enough information Answer 4 2.) Is f(x) = tan(x) continuous at x = 0? Yes No Not enough information Answer 4 3.) Find the value of c which will make the following function continuous: 3 2 -2 1/2 4.) Find the value of c which will make the following function continuous: 3 2 -2 1/2 5.) Find all vertical asymptotes of the following function: x = −2, 5 x = 3, 7 x = −1, 6 x = −1, 2 6.) Find all horizontal asymptotes of the following function: y = -3, 2 y = -3 y = 2, 3 y = 2 7.) Find the third derivative of f(x) = 4x^5 + 6x^3 + 2x + 1, with respect to x. 240x + 36 240 240x^2 + 36 x^2 + 36 8.) Find all points of inflection that occur on the function y = x^3 + 4x. x = 0 x = 0, 1 x = -1, 1 x = 2 9.) A baseball is hit into the air and has position function s(t) = -16t^2 + 25t + 4. Find the velocity. -32t + 25 -32t 32t - 25 -t + 25 10.) Find the acceleration of the baseball in #9. 32 109 -32 22 11.) The weight in kilograms of rocket fuel in a rocket launcher is given by W = (1/t) - (4/t^2), where t is time in seconds. At time t = 10 seconds, the amount of fuel in the launcher is decreasing at a rate of _____ kilograms per second. 0.01 0.002 1.343 1.701 12.) Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. When the diameter of the balloon is 20 cm, the radius of the balloon is increasing at a rate of ____ cm per minute. 1/80 80pi 1/80pi -1/80pi 13.) Find two nonnegative numbers whose sum is 9, such that the product of one number and the square of the other number is a maximum. 3, 6 3, 9 2, 6 2, 2 more

Voting Question: Help with Limits- (Early Calculus) 11th grade?

f(x) = x^2 - 3x +4 g(x) = x +2 1.) f [g(x) ] 2.) g [ f(x) ] Find The product (x^3 - 3x + 6) ( x^4 +2x +9) Simplify x divided by √3x - 1 +1 more

Resolved Question: Calculus question problem.. (with working steps).?

Find two non-negative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum. more

Resolved Question: pre calculus question #9?

Consider the vector v=(-6,13) Part I : Find the angle (in degrees) between v = (-6,13) and the x axis, which can be approximated as the vector (1,0) Part II : write v in the form ( | v | cos θ, | v | sin θ) Part III : Use the dot product of the vectors of v = (-6,13) and w= (-42,-34) to determine if they are orthogonal. more

Voting Question: Calculus Help, PLEASE!?

3.A manufacturer produces a product whose demand function is: P = 5000 - 2Q a.Determine the quantity of product that will maximize revenue. What is the corresponding price? Be sure to confirm that you have found a maximum. b.Suppose the manufacturer has fixed costs of $1,000 and the variable cost per unit is $500. Find the price of a unit that will maximize profit. Be sure to confirm that you have found a maximum. more

Resolved Question: URGENT CALCULUS question, please please please help?

y = (2x-5) ^ 4 (8x^2-5) ^ -3 I need to solve this using the Chain Rule, but I have no idea how to start, and incorportate product rule as well. Please help if you can. thanks more

Resolved Question: Calculus Product Rule Question?

So I have to find the derivative of f(x)= (2x+3)^4(3x-2)^(7/3) I used the product rule and came up with [8(2x+3)^3 * (3x-2)^(7/3)] + [(2x+3)^4 * 7(3x-2)^(4/3)] * means to multiply normally this works but i can't seem to simplify and factor any of this correctly, in my book the answer is (2x+3)^3 * (3x-2)^(4/3) * (38x+5) How did the answer come up with 38x+5? Is there some other formula for this more

Resolved Question: Recommend Calculus & Algebra book?

can any one recommend me the books covery following calculus & algebra topics: Pre-calculus 1permutations & combinations; expansion of (a+x)n using the sigma notation to express the sum of a series summing the terms of an arithmetic progression and a geometric progression 2interpolation and local approximation Elementary calculus 1the idea of a limit 2differentiation of polynomial, exponential and logarithmic functions 3product, quotient and "function of a function" rules for differentiation 4definite and indefinite integration of polynomial and exponential functions 5area under a curve 6methods of numerical integration 7integration by substitution and by parts More advanced calculus 1higher order derivatives 2finding turning points of simple functions with polynomial and exponential terms; curve sketching 3maximisation under constraints: method of Lagrange multipliers 4Taylor's theorem; power series expansion for exp(x) differentiation of definite integrals: Fundamental Theorem of the Calculus 5solving first order differential equations: exact, separable (including logistic), linear 6second order differential equations with constant 7coefficients: complementary function and particular 8integral Calculus of two variables 1partial derivatives of functions of two variables 2maxima and minima of functions of two variables 3double integrals and changing the order of double 4integrals Algebra 1matrix addition and multiplication 2determinant and inverse of a square matrix 3using matrices and vectors to represent linear equations solving simultaneous linear equations 4complex numbers 5linear difference equations with constant coefficients more

Resolved Question: Could someone differentiate a calculus problem using the product rule?

Here's the equation. y=(x^2+3x-1)(2-x) Easy ten points for anyone who gets this problem right. You don't need to show any work if you don't want too, but, you can if you fell like it. Just provide the answer please. Source " I need to simplify X^2+3x-1?" from Steve. Lutya2 since, you were the first one to answer this question you've earned yourself ten points. There is no point for any else to answer this question any more. I will explain why I asked this question as soon as I give you the ten points. It's not becasue; I didn't know how to solve this problem. more

Resolved Question: Challenge question: write xyz equation from three points?

Hello I am in Calculus, multivariable portion. I was given 3 points (1,0,0) , (0,2,0) and (0,0,2). Find a equation through the plane containing the points above. I was wondering if someone, without having taken calculus is able to solve this problem. I know you can take the points and make 2 vectors and take the cross product to find the normal vector and do the point slope form from there to get the equation. (BUT THATS CALCULUS) Anyone that challenges this question will be greatly appreciated. Thanks in advance more

Resolved Question: 12th grade Calculus Question Help?

1.Differentiate (x^2-5x+8) (x^3+7x+9) by expanding the product to obtain a single polynomial. Please explain with step by step working. 2.If ' u ' and ' v ' and ' w ' are functions of ' x ', then show that- d/dx (u . v . w) = du/dx v.w + u.dv/dx.w + u .v dw/dx Please explain step by step. Thank you in advance. (Awaiting reply) Thanx Bro!! It's -20x^3 BTW... more

Resolved Question: CALCULUS PROBLEMS PLEASE HELP!!!!!!!!!?

1) Use the Composite Rule to differentiate the function f(x) =e^cos x+sin x 2) use the Product Rule and your answer to part 1 to show that the function g(x) = (cos x+sin x-1)e^cos x +sin x (0<x<pi) has derivative g'(x)=cos^2x-sin^2x)e^cosx+sinx thanks more

Voting Question: Algebra problem!!!! ( 10 points for best answer)?

Two numbers have a difference of 8. Find the numbers if their product is a minimum. PLEASE DO NOT USE DERIVITIVES OR ANY SORT OF CALCULUS! more

Resolved Question: Two numbers have a difference of 8. Find the numbers if their product is a minimum.?

This is what I have so far: Let x be the first number, y be the 2nd number and m be the minimum. x - y = 8...1 xy = m PLEASE solve this problem without using calculus! since I'm only in Grade 10. more

Resolved Question: Calculus: dy/dx for the following:?

y = x^4 (x - 5 )^3 using the product rule Could you leave detailed workings. nice1 :) more

Voting Question: Hard calculus derivative question?

Find the derivative and simplify your result of f(x)= rad(x+1)/((2x-3)^2) Please use chain rule followed by product rule more

Resolved Question: Help with Pre-calculus! Can you help me with my take home math test?

Verify each identity. a) tan θ sin θ + cos θ = sec θ b) tan x / (1 - cos x) = csc x (1 + sec x) c) 2 tan x / (1 + tan2x) = sin 2x Find the exact value of each expression. a) sin 8° cos 22° + cos 8° sin 22° b) sin 75° c) sin (π/12) Write sin 3x cos 5x as a sum of trigonometric functions. Write sin 2x - sin 5x as a product of trigonometric functions. If sin θ = -(4/5) and θ is in quadrant III, find tan(θ/2). Solve each trigonometric function in the interval [0, 2π). a) 2 cos2x + 5 cos x + 2 = 0 b) sin 2x - cos x = 0 Find all solutions in the interval [0, 2π), correct to five decimal places. a) 5 cos 2x = 2 **ANY help is appreciated! Please try to explain or show what you're doing. Thanks!** more

Resolved Question: calculus word problem?

The daily marginal revenue function associated with selling x units of a certain product is given R'(x) = -0.2x + 74 , where R is measured in dollars/unit. Find the additional revenue realized when the production (and sales) level is increased from 100 to 200 units. more

Resolved Question: I need some help with at calculus problem. (vectors)?

Find 2 vectors parallel to <-3,-1,-7> whose magnitude is 59. I know that for 2 vectors to be parallel, their cross product must equal zero but other than that I am unsure on this problem. Help Please????? more

Resolved Question: CALCULUS: Find dy/dx for each of the following:?

a) y = x^4 (x - 5)^5 .............. Using the product rule b) y = e^3x/ x^3 .............. Using the Quotient Rule more

Resolved Question: calculus question!!! omg! wth!?

for vectors u=(1,2,-3) and v=(4,-5,6) find the angle theta between them and the cross product and its magnitude! pls asap more

Resolved Question: Calculus - Dot product Question?

The vectors a, b, and c are such that a + b + c = 0. Determine the value of a • b + a • c + b • c if |a| = 1, |b| = 2, and |c| = 3. Thanks. more

Resolved Question: I'm skipping Pre-Calculus and teaching it to myself, is this a good book?

Which one is good/better, or recommend a good one please. Nothing too expensive. (basically I'm graduating a year early and find it pointless to come back senior year for one math class, so I'm skipping ahead a year in math instead.) Choice numbah one: http://www.amazon.com/gp/product/0471378232/sr=1-27/qid=1243129195/ref=olp_product_details?ie=UTF8&me=&qid=1243129195&sr=1-27&seller= Choice numbah two: http://www.amazon.com/gp/product/0763737798/sr=1-12/qid=1243129023/ref=olp_product_details?ie=UTF8&me=&qid=1243129023&sr=1-12&seller= actually, i can skip it by studying over the summer. My school offers an option to test out of a class, where if you can take the standardized final exams and get an A or a B, you receive credit for that class. And its not so much about testing out as it is being prepared for the course. more

Resolved Question: My Calculus Answer Correct or Wrong?

These are my extra credit True or False questions and answer. I just want to know . My answers are correct or wrong? Thank You 1. The sum of two increasing functions is increasing. True 2. The product of two increasing functions is increasing. True 3. The composition of two increasing functions is increasing. True 4. If y = (x + 2)(x + 3)( x - 5) then d^4y/dx^4 = 0. True 5. If f '(c) and g' (c)are zero and h(x) = f(x)g(x) then h'(c) = 0. True 6. If f(x) is an nth-degree polynomial, then f^(n+1) = 0. True 7. The maximum of a function f(x) that is continuous on a closed interval can occur at two different values in the interval. True 8. If f(x) is continuous on a closed interval then it must have a minimum on the interval. True 9. If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x) + k, where k is a constant. True 10. If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x - k), where k is a constant. False more

Resolved Question: derivative/calculus rules proofs?

my friend (who actually has less general calculus knowledge than i do) proved that d/dx b^x=lnb*b^x and that d/dx x^n=nx^(n-1) and d/dx (f(x)+g(x))=d/dx f(x)+d/dx g(x) and some more but i've forgotten all of them it's late; im too tired to google this stuff. can you explain the proofs for these derivatives, and maybe the product, quotient, chain rule etc. thanks more

Resolved Question: Calculus Q: Let x, y and z be positive numbers whose product is 25. Find the minimum value of 9x + 5y + 3z?

Please do note that this is a calculus problem and therefore, x,y&z DO NOT HAVE TO BE WHOLE NUMBERS. Sorry for the caps but I've asked this question before and they all com up with x,y,z = 1,5,5, which is incorrect. It is likely the numbers are irrational. more

Resolved Question: Help with calculus homework?

Find two numbers differing by 38 whose product is as small as possible. more

Resolved Question: Calculus 3D Vectors, URGENT PLEASE HELP!!?

NOTE: One coordinate unit = 1000 feet. Also, the helicopter and the airplane are TWO SEPARATE moving vehicles. At noon (12:00 PM), a helicopter is observed from point A (7, 0, 0) in the direction of vector -4i + 2j + 5k, and simultaneously from point B (0, 4, 0.25) in the direction of vector 3i - 2j + 4.75k. One minute later (12:01 PM), the helicopter is observed from A in the direction of vector 6i + 7j + 5.005k and from B in the direction 13i + 3j + 4.755k. At 12:10 PM a different airplane is flying at the point Q (0, 0, 1) meaning that it is 1000 feet above the origin O. This airplane is traveling at 200 mph. Assuming that the helicopter continues to travel in a fixed direction at a fixed rate, (1) IN WHICH DIRECTION (vector) should the airplane fly (from point Q) in order to intercept the helicopter? (2) WHERE (coordinate) and at (3) WHAT TIME will this interception occur? I'm not sure if I should find the dot or cross product of the helicopter's vectors. I was also wondering if parametrizing those vectors and points would help at all, because I did that but didn't know how to proceed... Thank you so much if you can help me solve this or throw some pointers my way! This has been bugging me for so long :] more

Voting Question: Please help me with this calculus problem?

Find the derivative using the product rule: [axb=ab'+ba'] (t^1/3)(t^2+4) the answer is: (7t^2+4)/3t^2/3 I almost have the answer but Im messing up somewhere b/c I get: (t^1/3)(2t) + (t^2 + 4)/ (3t^2/3) I think my biggest pproblem w this is that I dont know how to multiply the first 2 terms b/c of the rational exponents....how do you multiply (t^1/3)(2t) ==== would it be 2t^4/3 ? Ok so where is this 7 coming from??? Thank you for any input, I greatly appreciate it. more

Voting Question: Im having trouble solving a calculus problem?

Find the derivative using the product rule: [axb=ab'+ba'] (t^1/3)(t^2+4) the answer is: (7t^2+4)/3t^2/3 I almost have the answer but Im messing up somewhere b/c I get: (t^1/3)(2t) + (t^2 + 4)/ (3t^2/3) I think my biggest pproblem w this is that I dont know how to multiply the first 2 terms b/c of the radical exponents....how do you multiply (t^1/3)(2t) ? Thank you for any input, I greatly appreciate it. *I meant rational, not radical THANK YOU!!! I GOT THE ANSWER!!!!!!!!!!THANK YOU THANK YOU THANK YOU LOL more

Resolved Question: minimizing and maximizing equations?

How would you do this pre-calculus problem? 1. The sum of two numbers is 124. Find the maximum product of the numbers. more

Voting Question: is anyone out there smart ? lol?

1. This type of software is designed for users who want to try a program before they purchase it. A. freeware B. open-source software C. shareware D. macros 2. A __________ program helps create long documents with separate chapters, a table of contents, and an index. A. spreadsheet B. graphics C. word processing D. web design 3. A __________ is a contiguous group of characters, words, lines, sentences, or paragraphs in a document that you can mark for editing or formatting. A. page B. block C. chapter D. sentence 4. A __________ is a named set of characters that have the same characteristics. A. type face B. type style C. font D. pica 5. This type of program can be used to create signs for a neighborhood garage sale. A. Presentation B. Word processing C. Spreadsheet D. Database 6. In a spreadsheet program, you work in a document called a __________ . A. workbook B. column C. cell D. worksheet 7. You can create __________ to perform basic arithmetic, calculus, or trigonometric operations. A. cells B. worksheets C. labels D. formulas 8. Spreadsheet programs generally hold _________ data than do database programs. A. more B. less C. the same amount of D. more complicated 9. Database programs hold data in ___________ . A. spreadsheets B. workbooks C. queries D. tables 10. In a database, the row represents a _____________. A. field B. record C. data set D. number 11. In a presentation program a(n) __________ is a single-screen image that contains a combination of text, numbers, and graphics. A. text box B. slide C. frame D. object 12. What does the acronym PIM stand for? A. Professional information management B. Professional instant messaging C. Personal information management D. Personal instant messaging 13. Which of the following tools allows you to communicate immediately with another person or people? A. Instant Messaging B. E-mail C. Chat rooms D. Both A and C 14. A __________ is a list of commands, keystrokes, or other actions that are used to automate a task within a program. A. shortcut B. file C. project D. macro 15. A(n) __________ is software you purchase that solves multiple tasks. A. suite B. stand-alone program C. open-source program D. freeware program 16. If you magnify a(n) __________, you can see its individual pixels. A. vector graphic B. bitmap C. DXF D. EMF 17. Mathematical equations describing the size, shape, thickness, position, color, and fill of lines or closed graphical shapes are called ___________. A. images B. objects C. vectors D. algorithms 18. The term bitmap originated with large books of reproducible images. Answer True False 19. This type of graphics program allows you to change the “canvas” texture of a picture. A. Paint program B. Photo-editing program C. Draw program D. Computer-aided design program 20. All objects created in a draw program consist of a(n) ________ and a _______. A. outline, fill B. shape, background C. line, curve D. color, shape 21. In a photo editor, you can repair scratches using the __________ tool. A. mask B. airbrush C. stamper D. eraser 22. The acronym CAD can stand for any of the following EXCEPT which term? A. Computer-aided design B. Computer-aided drafting C. Computer-aided drawing D. Computer-aided device 23. CGI programs are used by professional __________. A. architects B. animators C. engineers D. contractors 24. The bitmap format supports up to 24-bit depth color, or over ___________ different colors. A. 12 thousand B. 12 million C. 16 million D. 24 million 25. This graphic type is commonly only found in the Macintosh family of operating systems. A. bmp B. jpg C. gif D. pict 26. Blueprints are usually created using __________ software. A. CAD B. paint C. CGI D. draw 27. To create a prototype of a new product, an engineer or designer might use a CAD program. Answer True False 28. Using more than one medium in a project is commonly referred to as __________. A. multimedia B. CAD C. photo-realistic D. CGI 29. A __________ is a predesigned document that already has coordinating fonts, a layout, and a background. A. template B. model C. ruler D. guide 30. Which of the following is NOT a standard format for bitmap graphics? A. JPEG B. TIFF C. PTX D. GIF more

Resolved Question: multivariable calculus proof question?

The norm on Rn can be defined in terms of the dot product by the formula ||x|| = √x • x. Show that the reverse is true. That is, find a formula for x • y involving the norms of vectors (||x||, ||y||, ||x+y||, and ||x−y|| for example), and without using coordinates. more

Resolved Question: multi-variable calculus using dot product?

any hints would be appreciated, Using dot product, show that for x,y in Rn, the formula 2||x||^2 + 2||y||^2 = || x+y ||^2 + || x-y ||^2 holds. more

Voting Question: Calculus/Vectors Question?

Vectors A and B are UNIT VECTORS. |A + B| = sqrt(3). Find (2A - 5B) * (B + 3A)......* is the Dot Product between them btw. more

Resolved Question: can you translate this japanese sentence(s)?

you dont have to translate them all, but just a few.... please translate in ENGLISH, please, i cant read japanese.... for example "my name is john" ---> "ore no namae wa john desu" 1 - i dont wanna talk to traitors 2 - i dont feel like talking to cowards 3 - i dont talk to fools 4 - if i collect 10 coupons, is the discount rate 50%? 5 - my child ran away from home, and im not sure what to do 6 - we're not sure of the exact date when the war will be over 7 - astronomy, biology, physics, anatomy, ecology, and geology 8 - algebra, geometry, trigonometry, and calculus 9 - why are you hiding between those walls? 10 - is it evil to steal from rich people to help the poor? 11 - would you consider this product safe? 12 - sword, spear, bow & arrow, axe, catapult, cannon, and 13 - stomach, chest, armpit, neck, knee, elbow, ankle, and body 14 - face, ears, eyes, nose, mouth, hair, and head 15 - toe, finger, fingernail, toenail, thumb, and knuckle 16 - mustache and beard 17 - fireman, nurse, janitor, driver, taxi driver, and contruction worker 18 - the color brown 19 - clock, and watch 20 - map, portrait, art, drawing, and direction 21 - calender 22 - law, economy, politics, government, country, state, and capital 23 - democracy, republic, and communism 24 - war, negotiation, truce, battle, victory, defeat, loss, and retaliation 25 - building, infrastructure, house, city, town, local, and street more

Resolved Question: calculus - differentiation involving chain rule and product rule?

I'm quite stuck: the question is this: differentiate 3x(2x-1)^(3) and i got something like 96x^(3) - 98x^(2) + 36x - 3 so, why is the actual answer: 3(2x-1)^(2) * (8x-1) ??? please show working! more

Resolved Question: Pre-Calculus,Find the Derivative.?

I need help finding the derivative of this fuction,using the Product Rule.This is the link so you can see it http://img19.imageshack.us/my.php?image=calcul.png the function is read as f of x is equal to radical x plus four,cubed root x,times x to the fifth,minus 11x to the eighth power more

Resolved Question: Question Worth More than 10 points, but I can't give it to you, so oh well? Conceptualizing Volumes by Shell?

I'm a student currently taking 2 Calculus classes (because I'm a loser and really suck at math.) The current topic in one of my classes is volumes of plane shapes being rotated across different axes (multiple of axis? Herrrrr~) The product is of course a 3-D shape. Two ways of finding these volumes are by the disc method and the shell method. Disc: Pi(r)^2 ~> Pi (int{f(x)}^(2))dx Shell: 2Pi(r) ~> 2Pi (int{f(x)})dx ~> 2Pi int(p(x)h(x)dx) Where p is the function of the radius, and h is the function of the height. What my problem is, is how to understand what the equations will be for the height and the radius. Sometimes I can visualize it easily, other times not. I'm pretty sure it has something to do with the voids produced within the new shape, but I don't know how to interpret it into mathematical terms. Example: Given y=1/x and the bounding regions of x=1, and x=2, what is the volume of the shape produced by rotating it about the x-axis? Sometimes I can understand it after I've looked at the equation in the answer section... Another Example: Given the equation y = x^(1/2) and the bounds of x=0, x=4, find the volume of the solid produced by rotating the graph about the: a. y-axis b. x-axis c. x =4 d. x =5 e. y =2 f. y = -1 I know I'm asking a lot of questions, and you don't necessarily have to answer them all to get the 10 points. What I need most is help on understanding the equation for the radius and the equation for the height. If your answer helps me do that, then you get the 10 points. :) Work will probably help me understand the most, so goodluck! more

Resolved Question: Depression, short term memory loss, inability to retain information?

I've self-diagnosed myself with depression for reasons I will not bother to explain. I was a very good student in school, not so much because of good grades (which I never cared about) but because I could understand problems and come up with solutions very quickly, and I had a very good memory. So much so, I rarely studied for exams and did well anyway. I'm now in university, studyiing to become a mathematician. I realize very rationally being the best in school is hardly being the best in a good university, that much I can take so I don't mind knowing there are people out there better than me. I'm worried because my ability to remember, use and process information dosn't seem to be half as good as it used to. I've failed subjects that should've been easy, and no matter how hard I study, I can't seem to remember enough during exams. Lately, I've been even more worried: 1) during a vector calculus exam, I couldn't for the life of me remember the integral of ln(x). It doesn't make sense if you don't know much about calculus, but just to make things clearer, it's kinda like forgetting your time tables. It's something you're supposed to remember because you'll need it very often. I could remember the derivative, and part of the process of figuring out the integral, but I tried several times and got no answer. I passed the exam, only just, but I could've done much better. 2) During another exam, linear algebra 2, I failed to get the product of two matrices right. I multiplied them at least 7 times, and it took me about 10 to get it right. Again, it's something that shouldn't be so hard, as it was a 4x4 matrix. 3) Even more worrying still, during class on wednesday a teacher mentioned we were having a partial exam on friday, yesterday. Final exams are coming up, and she sent two emails, one saying we were trying to set the date of the final exam for may the 14th at 10am and another one saying in which classroom and what time the exam was. I figured she meant the final exam so I made a note with the information for may 14th. I went to class on friday, but the classroom was empty and I saw no one around. I remember hearing her say in class that we were doing exercises from the book, so I got some ready. I understand now she meant the classroom and time to refer to the exam, as well as preparing exercises because she sent me an e-mail asking why I didn't go to the exam. I haven't skipped class, I've been a couple of minutes late (15 min late tops), but I'm sure I'd remember being told of an exam. My question, more specifically then, is can my depression be causing this? Are there good reasons to go to a doctor or am I just paranoid? What can I do to improve my memory and my ability to retain information? I looked online, and it seems (though I saw no good references) minor concussions can cause enough damage to cause the effects I'm talking about. In case there's any relevance, I was once hit pretty hard on the head about 3 years ago... Weird incident where I was sitting down on the grass in a park with some friends and a big dog ran right at me and we bumped heads... Made me dizzy for about an hour, but I didn't think it was serious so I didn't go to a doctor. It sounds like I'm hypochondriac, I know, and I also reckon that to some extent I'm not supposed to be as smart as I was before. Just for the record, in case it made any difference, I'm not on drugs, I don't drink (I just don't like the taste of alcoholic beverages, so I don't lose neurons due to getting ridiculously drunk), and the only pills I'm taking are some birth control pills my dermatologist prescribed for acne, something to do with hormones and lipid producing glands in my face. I'm 20 years old (which shouldn't be that old), and though I doubt it's likely to be kicking in now, there's a history of alzheimer's disease in my family. I'd like straightforward answers based on facts and studies in preferably western medicine. I'm not a fan of alternative medicine, herbs, crystals or whatever, and please don't tell me to pray to God that things get better for me, because as much as I respect your belief in a God (whichever it may be) I need you to respect my decision not to believe in any. Thanks in advance for any answers. more

Resolved Question: Calculus Question regarding product rule to differentiate?

using the product rule to differentiate f(t) = (1 - t2) (1 - 3/t2) i know u = 1-t2 so du/dt = -2t and v= 1-3/t2 but i can't figure out what dv/dt= i keep thinking its 6t but its not.... Anyone? more

Voting Question: Pre-Calculus question?? PLEASE!?

(cosx-cosy)/(sinx+siny)=(sinx-siny)(cosx+cosy) Prove the identity... hmm i dont know if this helps but we only know basc trig identity, Pythagorean, sum and difference, double-angle, half angle, and product to sum identities... PLEASE HELP ME PLEASE!!!!!! i dont know if u can see the question... its (cosx-cosy)/(sinx+siny)/(sinx-siny)/(cosx+cosy) AGHH the 2nd half is /-siny /(cosx+cosy) (cosx-cosy)/(sinx+siny)=(sinx-siny)(cosx +cosy) there! more

Resolved Question: calculus / business math help...please?

for a monopolist's product, the demand function is p = 85 - 0.05q and the cost function is c = 600 + 35q At what level of output will profit be maximized? At what price does this occur, and what is the profit? can you please answer me with step by step as to how you got the answer thanks a million in advanced more

Resolved Question: Calculus word problem (rate of change, revenue)?

Ok i'm not sure how easy or hard this problem is, here it goes A factory is increasing production of a product at 200 units per week. The weekly demand function is p= 100 - 0.001x where p is price per unit and x is the number of units produced in a week. Find the rate of change of the revenue with respect to time when weekly production is 2000 units. Ok so i could be wrong but this is my take on the problem. Firstly R = xp so my first step would be R= x(100-0.001x) I believe i'm suppose to find dr/dx and then plugin x = 2000 so what i did was I began to find the derivative of R= x(100-0.001x) R= 100x-0.001x^2 dr/dx= 100 - 0.002x then I replaced x with 2000, and got dr/dx= 4 Would 4 be my answer here? Also i never used the number 200 which is mentioned at the beginning of the problem, i don't think they would have included 200 if i didn't need it, unless they are trying to trick me. Any help is appreciated. more

Voting Question: calculus vectors dot product?

prove that the triple scalar product of the vectors u, v and w has the property that u (dot) (v x w)= (u x v) (dot) w PS.the above statement is all in vectors..i just dunn how to put the vector sign on it and also the dot :S sry plaz help..any answers or suggestions are welcomed ty in adv more

Resolved Question: Stuck with Calculus 1. Anybody like doing this stuff? haha?

the question tells me to find teh derivative of y with respect to x. the formula is y=(1+4x)e^(-4x) I used the product rule to give me (1+4x)-4e(-4x)+4(e^-4x) I am stuck where to go now to find y'(x) Any ideas? any advice would be greatly appreciated! -16 * x * e^(-4x) is apparently wrong also more

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