Thursday
July 24, 2014

# Homework Help: Math: Calculus

Calculus
Find the equation of the tangent line to the curve (piriform) y^2=x^3(4−x) at the point (2,16−−ã). a. Find dy/dx at x=2. dy/dx= b. Write the equation of the tangent line to the curve.
Tuesday, June 25, 2013 at 5:25pm

Calculus
Find dy/dx by implicit differentiation: cos(x−y)=−4xe^x
Tuesday, June 25, 2013 at 10:15am

Calculus
Find dy/dx by implicit differentiation for the following 2x^2y+3y=-1
Tuesday, June 25, 2013 at 10:10am

The motion of a spring that is subject to dampening (such as a car's shock absorber)is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion for a point on such a spring is s(t)=3∗e−2tsin(3ðt) ...
Monday, June 24, 2013 at 10:26am

Calculus 2
(x^3+2x^2-15x+1)/(x^2+2x-15) from 0 to 7
Sunday, June 23, 2013 at 9:27pm

Calculus 2
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g and 3.14 for π. If you enter your answer in scientific notation, round the decimal value to two decimal places. Use equivalent rounding if you do not enter your answer in ...
Saturday, June 22, 2013 at 12:22am

Calculus 2
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about x = 4. y = 3 x^4 y = 0 x = 2
Friday, June 21, 2013 at 9:59pm

math-calculus 2
Consider the given curves to do the following. 64 y = x^3, y = 0, x = 4 Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 1.
Friday, June 21, 2013 at 5:23pm

calculus
1.Ruth has 240 feet of fencing available to enclose a rectangular field. Express the area A of the rectangular field as a function x, where x is the length of the field. 2. For what value of x is the area largest? 3. What is the maximum area?
Thursday, June 20, 2013 at 10:03pm

Differential Calculus (first part)
if g(x) = cos2x find g(-x)
Thursday, June 20, 2013 at 9:37pm

Calculus
Find the linear approximation L(x) of ln(x)at the point a = 12.
Thursday, June 20, 2013 at 9:17pm

Calculus
The interval [0,4] is partitioned into n equal subintervals, and a number x_i is arbitrarily chosen in the i^th subinterval for each i. Then.... lim_(n → ∞) ∑_(i = 1 → n)[2x_i+8)/n]=???
Thursday, June 20, 2013 at 7:03pm

Calculus (Arc Length)
Consider the helix parametrized with the vector equation r(t)=cos t i+ sin t j + t k. The length L of the helix between the points (1,0,0) and (1,0,6π) is equal to aπ. What is the value of a^2?
Thursday, June 20, 2013 at 10:16am

Calculus
∫10 to 21,f(x)dx-∫10 to 14, f(x)dx=∫a to b,f(x). where a=?,b=?
Thursday, June 20, 2013 at 8:55am

Calculus
The velocity function is v(t)=t^2-5t+6 for a particle moving along a line. Find the displacement of the particle during the time interval [-3,6].
Thursday, June 20, 2013 at 8:47am

diffirential calculus
express the surface of a right circular cylinder a function of its volume assuming the height is constant
Thursday, June 20, 2013 at 5:15am

Calculus
The radius of a circular disk is given as 51 cm with a maximum error of 0.04 cm. Use differentials to estimate the maximum error and percent error in the calculated area of the disk.
Wednesday, June 19, 2013 at 3:56pm

Calculus
Find the Taylor Polynomial of order 1 for the function f(x)=arctan(x/5) in powers of (x-5). Also find the remainder R1(x) as a function of x and c.
Wednesday, June 19, 2013 at 11:29am

Calculus
By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B) 1-(2^2)/(2!)+(2^4)/(4!)-(2^6)/(6!)+...+(​(-1)^(k)2^(2k))/((2k)!) +...=
Tuesday, June 18, 2013 at 10:24pm

Calculus
Find the 3rd order for the taylor polynomial in powers of x for the function f(x)=sinh2x and find the remainder as a function of x and c. P3(x)=? R3(x)=? What's the kth term expression?
Tuesday, June 18, 2013 at 8:46pm

Calculus
Find the general expression of the kth nonzero term in the taylor series f(x) = 3/(1+x), for k= 0, 1, 2,...
Tuesday, June 18, 2013 at 8:44pm

Calculus
The motion of a spring that is subject to dampening (such as a car's shock absorber)is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion for a point on such a spring is s(t)=3∗e^(−2t)sin(3ð...
Tuesday, June 18, 2013 at 7:04pm

Calculus
The management of the UNICO department store has decided to enclose a 917 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will ...
Tuesday, June 18, 2013 at 4:35pm

Calculus
Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = −x2 + 2x + 3 on [3, 6] maximum minimum
Tuesday, June 18, 2013 at 4:30pm

Calculus
Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. (If an answer does not exist, enter DNE.) f(t) = 7 t + 3/t relative maximum (x, y) = relative minimum (x, y) =
Tuesday, June 18, 2013 at 4:28pm

Calculus
Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.
Tuesday, June 18, 2013 at 2:41pm

Calculus
A fence 3 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building. Answer the following: The distance along the ladder to the top ...
Tuesday, June 18, 2013 at 2:13pm

Calculus
Find the point on the line 4x+3y-4=0 which is closest to the point (5,2)
Tuesday, June 18, 2013 at 2:08pm

Calculus
For what values of x with 0¡Üx¡Ü2¦&ET​H; does the graph of f(x)=x+4sin(x) have a horizontal tangent?
Tuesday, June 18, 2013 at 10:39am

Calculus
Find the equation of the tangent line to the curve y=2tan(x) at the point (pi/4,2).
Tuesday, June 18, 2013 at 10:38am

Calculus
An arithmetic progression has terms a8 =23 and a20 =83 . What is the value of the term a12
Tuesday, June 18, 2013 at 10:13am

Calculus
Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x^3 + 3 x^2 - 1 on [-3, 1]
Monday, June 17, 2013 at 8:21pm

Calculus
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price/compact disc. The equation p = -0.00048 x + 7\ \ \ \ $$0<=x<=12,000$$ where p denotes the unit price in...
Monday, June 17, 2013 at 8:21pm

Calculus
The weekly demand for the Pulsar 25-in. color console television is given by the demand equation p = -0.03 x + 571\ \ \ \ $$0<=x<=12,000$$ where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated ...
Monday, June 17, 2013 at 8:21pm

Calculus
Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. P(x) = -10 x^2 + 1780 x - 54,000 To maximize the monthly rental profit, how many units should be rented ...
Monday, June 17, 2013 at 8:20pm

Calculus
The quantity demanded each month of the Sicard wristwatch is related to the unit price given by the equation below, where p is measured in dollars and x is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? (Round your answer to the ...
Monday, June 17, 2013 at 7:59pm

Calculus
The management of the UNICO department store has decided to enclose a 917 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will ...
Monday, June 17, 2013 at 7:56pm

Calculus
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 10 in. wide, find the dimensions of the box that will yield the maximum volume. (Round your ...
Monday, June 17, 2013 at 7:56pm

Calculus
A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 37¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 13¢/square foot, determine the dimensions of the box that ...
Monday, June 17, 2013 at 7:55pm

Calculus
Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) passes through the point (0,−6) ...
Monday, June 17, 2013 at 3:45pm

Calculus
Find the values of a ,b, and c in the quadratic function p(x)=ax^2+bx+c such that p(2)=6, p'2)=2, and p''(2)=3. a = b = c =
Monday, June 17, 2013 at 3:44pm

calculus
find equation of tangent line for x^(1/3) + y^(1/2)=2 at point (1,1)
Sunday, June 16, 2013 at 7:32pm

calculus
find a point on the curve x^3 + y^3 =2xy other than the origin at which tangent line is horizontal
Sunday, June 16, 2013 at 7:31pm

calculus
estimate ln(e^2+0.1)-ln(e^2)
Sunday, June 16, 2013 at 6:51pm

calculus
estimate change in f using the linear approximation and compute both error and the % error f(x)= (3+x)^1/2 a=1 change in x=0.5
Sunday, June 16, 2013 at 6:39pm

calculus
estimate change in f using the linear approximation and compute both error and the % error f(x)= (3+x)^1/2 a=1 change in x=0.5
Sunday, June 16, 2013 at 4:54pm

pre calculus
Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This is the problem I am stuck on: f(x)= x^...
Sunday, June 16, 2013 at 1:32pm

pre calculus
Hi, I am having a problem trying to find and understanding how to find the extreme values. I have a problem which I can't do. Will someone please explain for me how to do it. I would like to be able to do other similar problems. This is the problem I am stuck on: f(x)= x^...
Sunday, June 16, 2013 at 1:32pm

calculus
which number should be subtracted from each of the three numbers 5, 15, and 50 so that the resulting three numbers form a geometric progression?
Saturday, June 15, 2013 at 1:45am

Calculus
Find the values of a , b , and c in the quadratic function p(x)=ax2+bx+c such that p(2)=6, p'(2)=2, p"(2)=3
Friday, June 14, 2013 at 7:08pm

Calculus
Find the values of a , b , and c in the quadratic function p(x)=ax^2+bx+c such that p(2)=6, pŒ(2)=2, and pŒŒ(2)=3.
Friday, June 14, 2013 at 5:56pm

Calculus
Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point. (x - y - 1)3 = x; (1, -1) y =
Thursday, June 13, 2013 at 10:06pm

Calculus
Follow the steps below for the given function. (Do not use mixed numbers in your answers.) 2x + 5y = 1 Solve the equation for y. y = Differentiate this equation with respect to x. y ' = Complete the steps below to implicitly take the derivative of the original equation. 2x...
Thursday, June 13, 2013 at 10:03pm

Calculus
Let f be the function defined as follows. $y = f(x) = {\color{red}5} x^2 -{\color{red}9} x +{\color{red}10}$ (a) Find the differential of f. dy = (b) Use your result from part (a) to find the approximate change in y if x changes from 2 to 1.97. (Round your answer to two ...
Thursday, June 13, 2013 at 8:53pm

Calculus
Let f be the function defined as follows. $y = f(x) = \sqrt{{\color{red}3} x +{\color{red}10}}$ (a) Find the differential of f. dy = (b) Use your result from part (a) to find the approximate change in y if x changes from 4 to 4.1 (Round your answer to three decimal places.). ...
Thursday, June 13, 2013 at 8:53pm

Calculus
The volume of a spherical cancerous tumor is given by the following equation. V(r) = (4/3)pi r^3 If the radius of a tumor is estimated at 1.4 cm, with a maximum error in measurement of 0.003 cm, determine the error that might occur when the volume of the tumor is calculated. cm3
Thursday, June 13, 2013 at 8:52pm

Calculus
A car leaves an intersection traveling west. Its position 5 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 5 sec later is 27 ft from the intersection. If the speed of the cars at that ...
Thursday, June 13, 2013 at 8:51pm

Calculus
The total worldwide box-office receipts for a long-running movie are approximated by the following function where T(x) is measured in millions of dollars and x is the number of years since the movie's release. T(x) = (120x^2)/(x^2 + 4) How fast are the total receipts ...
Thursday, June 13, 2013 at 8:16pm

Calculus
Suppose f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = -1, g(1) = -2, and g '(1) = 3. Find the value of h '(1). h(x) = (x2 + 11) g(x) h '(1) =
Thursday, June 13, 2013 at 8:16pm

Calculus
The relationship between the amount of money x that Cannon Precision Instruments spends on advertising and the company's total sales S(x) is given by the following function where x is measured in thousands of dollars. S(x) = -0.002x3 + 0.9x2 + 4x + 500 (0 x 200) Find the ...
Thursday, June 13, 2013 at 8:15pm

Calculus
The demand function for the Luminar desk lamp is given by the following function where x is the quantity demanded in thousands and p is the unit price in dollars. p = f(x) = -0.1x2 - 0.3x + 39 (a) Find f '(x). f '(x) = (b) What is the rate of change of the unit price ...
Thursday, June 13, 2013 at 8:14pm

Calculus
Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 15x2 (x, y) = ( , ) (smaller x-value) (x, y) = ( , ) (larger x-value)
Thursday, June 13, 2013 at 8:14pm

Calculus
Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x) = -8/5 x^2 + 7 x + 7;(-1, -8/5) slope tangent line y =
Thursday, June 13, 2013 at 8:12pm

Calculus
Let f(x) = 4x5/4 + 10x3/2 + 9x. Find the following. (a) f '(0) = (b) f '(16) =
Thursday, June 13, 2013 at 8:11pm

Calculus
Given that f(x)=x^8h(x) h(−1)=5 hŒ(−1)=8 Calculate fŒ(−1).
Thursday, June 13, 2013 at 9:52am

Calculus
The equation of motion of a particle is s=4t^3−7t, where s is in meters and t is in seconds. Find a) the velocity of the particle as a function of t : v(t)= b) the acceleration of the particle as a function of t : a(t)= c) the velocity after 5 seconds d) the acceleration...
Thursday, June 13, 2013 at 8:42am

Calculus
Find an equation for the tangent line of the function f(x)=6+10xe^x at the point (0,6).
Thursday, June 13, 2013 at 6:40am

Calculus
Consider the vector field: F(x,y)=2xyi+x^(2)j Integrate F over a path starting at (0,0) and ending at (2,2).
Wednesday, June 12, 2013 at 8:56pm

Calculus
Let f(x,y)=sqrt(1-x^2) and R be the triangular region with corners (0,0), (1,0), and (1,1). Evaluate the double integral(R) f(x,y)dA.
Wednesday, June 12, 2013 at 8:53pm

Calculus
Find an equation for the tangent line of the function y=x+(4/x) at the point (2, 4). The equation of the tangent line is . You may enter the equation in any form.
Wednesday, June 12, 2013 at 6:11pm

Calculus
Given that f(x)=x^8h(x): h(−1)=5 hŒ(−1)=8 Calculate fŒ(−1)?
Wednesday, June 12, 2013 at 5:37pm

Calculus
A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs 42¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 26¢/ft2. Letting x denote the length of one side of the base, find a function...
Tuesday, June 11, 2013 at 3:32pm

calculus
solve for the second derivative and set to zero f"(x) = ((x^2-4)*sin(2x)- [(2x)(1+cos^2(x))]/ ((1+cos^2(x))^2) i dont know how to set it to zero and solve i get this: (x^2-4)(sin(2x))= (2x)(1+cos^2(x)) thanks for help i did not get a clear response earlier so i am ...
Tuesday, June 11, 2013 at 9:02am

calculus
solve for the second derivative and set to zero f"(x) = ((x^2-4)*sin(2x)- [(2x)(1+cos^2(x))]/ ((1+cos^2(x))^2) i dont know how to set it to zero and solve i get this: (x^2-4)(sin(2x))= (2x)(1+cos^2(x)) thanks for help
Monday, June 10, 2013 at 11:36pm

Without solving , determine the points of intersection of the line r= (5,-9,3) +k (1,-12,2] and the plane [x,y,z]= (4,-15,-8) + s[1,-3,1] + t[2,3,1], if any exist.
Monday, June 10, 2013 at 5:18pm

Calculus grade 12 lines and planes
Find the value of k so that the line [x,y,z] = [2,-2,0]+ t[2,k,-3] is parallel to the plane kx +2y - 4z= 12
Monday, June 10, 2013 at 5:12pm

Determine the value of k such that the points (4,-2,6), B(0,1,0) and C(1,0,-5) and D (1,k,-2) lie on the same plane.
Monday, June 10, 2013 at 3:36pm

Find the equation of the plane that passes through the point (3,7,-1) and is perpendicular to the line of intersection of the planes x-y-2z+3=0 and 3x-2y+z+5=0
Monday, June 10, 2013 at 3:32pm

calculus
simplify aab-3/Ba^2b-2
Sunday, June 9, 2013 at 11:59pm

Pre-Calculus
can someone help me with figuring out my math and explaining it to me. or How to use the calculator with the problems ?
Sunday, June 9, 2013 at 8:48pm

Calculus
If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x + . Check your answer for ...
Sunday, June 9, 2013 at 1:12am

Calculus
If an arrow is shot straight up from the surface of the moon with an initial velocity of 100 ft/s, its height in feet after t second is given by s(t)=(100t)−(83/100)(t^2). Use the limit definition of the derivative to find the answers to the following questions. Find the...
Saturday, June 8, 2013 at 10:12pm

calculus
In the computer game, there must be a ramp that is 2 m wide, with height 3 m and length. 5 m. Assume that one corner of the bottom of the ramp is at the origin.
Saturday, June 8, 2013 at 11:49am

Calculus
Let f(x)=−4−3x+2x^2. Use the limit definition of the derivative to find find fŒ(a)
Saturday, June 8, 2013 at 7:00am

calculus
find the absolute maximum and minimum of sqrt 3 x^2/36 + (1-x)^2/32
Saturday, June 8, 2013 at 1:10am

Calculus
I'm trying to find the radius of convergence for \$(x-2)^n/(2x+1) I did the ratio test and ended up with: absolute value[(x-2)/(2x+1)]<1 How would I solve for the inequality at this point?
Friday, June 7, 2013 at 9:57pm

Calculus
Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. f(x) = 16 - 10 x Step 2: f(x + h) - f(x) = Step 4: f'(x) = lim(h->0)(f(x + h)- f(x))/h =
Friday, June 7, 2013 at 9:19pm

Calculus
The demand function for Sportsman 5 X 7 tents is given by the following function where p is measured in dollars and x is measured in units of a thousand. (Round your answers to three decimal places.) p = f(x) = -0.1x^2 - x + 40 (a) Find the average rate of change in the unit ...
Friday, June 7, 2013 at 3:20pm

Calculus
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/(4 x) at (1,(15/4) m = y =
Friday, June 7, 2013 at 3:20pm

Calculus
A major corporation is building a 4325 acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Clove's population (in thousands) t yr from now will be given by...
Friday, June 7, 2013 at 3:19pm

Calculus
The concentration of a certain drug (in mg/cm3) in a patient's bloodstream t hr after injection is given by the following function. C(t) = (0.6 t)/(t^2 + 5) Evaluate the limit. (If an answer does not exist, enter DNE.)
Friday, June 7, 2013 at 3:19pm

Calculus
Find the indicated limit given the following. lim_(x->a)f(x)= 10 and lim_(x->a)g(x) = 12 lim_(x->a)(f(x)*g(x)) =
Friday, June 7, 2013 at 3:18pm

Calculus
Find the indicated limit given the following. lim_(x->a)f(x) = 8 lim_(x->a)(2f(x)) =
Friday, June 7, 2013 at 3:14pm

Calculus
Find the indicated limit. lim_(x->-63.5)(root3(2x + 2))
Friday, June 7, 2013 at 3:13pm

Calculus
Complete the table by computing f(x) at the given values of x. (Round your answers to three decimal places.) f(x) = 2x^2 - 7 x 6.9 6.99 6.999 7.001 7.01 7.1 Use these results to estimate the indicated limit (if it exists). (If an answer does not exist, enter DNE.) lim_(x->7...
Friday, June 7, 2013 at 2:53pm

Calculus
Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the following function. P = f(t) = 3t^2 + 2t + 1 Find the rate of population growth at t = 10 min. bacteria per minute
Friday, June 7, 2013 at 2:46pm

Calculus
Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = x^2 - x + 1 text( on ) [-1,12]; M = 21
Friday, June 7, 2013 at 2:44pm

Calculus
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/4 x at (1,15/4)
Thursday, June 6, 2013 at 7:08pm

Calculus
y = f(x) = x^2 - 6 x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 2 to x = 3 from x = 2 to x = 2.5 from x = 2 to x = 2.1 (b) Find the (instantaneous) rate of change of y at x = 2.
Thursday, June 6, 2013 at 6:58pm

Calculus
Use Green's theorem to evaluate the integral: y^(2)dx+xy dy where C is the boundary of the region lying between the graphs of y=0, y=sqrt(x), and x=9
Thursday, June 6, 2013 at 3:10pm

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