Saturday
June 25, 2016

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

Calculus 1 optimization
A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence? ft (...
Thursday, November 5, 2015 by TayB

Pre-Calculus
Write the standard form of the equation of the line that passes through the point (-4, -2) and is perpendicular to the graph of 3x - 2y + 9 = 0.
Thursday, November 5, 2015 by Tay

Calculus 1
The rate (in mg carbon/m^3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = (120I)/(I^2 + I + 4) where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
Thursday, November 5, 2015 by TayB

Calculus
use tangent line approximation (linear approximation) to estimate The cube root of 1234 to 3 decimal places. Hint: the equation should be y=f'(x0)(x-x0)+f(x0) 11^3=1331 can be easily computed using binomial theorem. I used linear approximation and got 10.733, but it is not...
Wednesday, November 4, 2015 by Henry

Calculus
A box with a square base and no top is to be built with a volume of 4000 in3. Find the dimensions of the box (Length, Width, Height) that requires the least amount of material. How much material is required at the minimum?
Wednesday, November 4, 2015 by E

Calculus 1
Locate the absolute extrema of the function f(x)=Sinpix on the closed interval [1,1/3]
Wednesday, November 4, 2015 by Justin

Calculus
Find the limit as x approaches 0+ of (lnx)/x using L'hospitals rule. When I do this, I keep getting stuck at 1/0 when you plug back into the equation after doing l'hospital once.
Wednesday, November 4, 2015 by Callie

Calculus
Evaluate ∫ (cos(x))^(1/2)sin(x)dx Let u = cos(x)? ∫ (u)^(1/2)sin(x)dx = ∫ [2u^(3/2)/3]sin(x)dx ∫ [2cos(x)^(3/2)/3] (-cos(x)) dx? I thought this involved the FTC, but now I'm thinking that's false.
Wednesday, November 4, 2015 by Justin

Calculus
Alright, I want to see if I understand the language of these two problems and their solutions. It asks: If F(x) = [given integrand], find the derivative F'(x). So is F(x) just our function, and F'(x) our antiderivative? 1) F(x) = ∫(2, x) [t^(3)+1]^(1/2)dt Let u...
Wednesday, November 4, 2015 by Justin

calculus
A Norman window is constructed by adjoining a semicircle to the top of a rectangular window . (The diameter of the semicircle is the same as the width of the rectangular) If the perimeter of the Norman window is 20 ft, find the dimensions that will allow the window to admit ...
Wednesday, November 4, 2015 by Beth

Calculus
Gloria would like to construct a box with volume of exactly 45ft^3 using only metal and wood. The metal costs $15/ft^2 and the wood costs $6/ft^2. If the wood is to go on the sides, the metal is to go on the top and bottom, and if the length of the base is to be 3 times the ...
Wednesday, November 4, 2015 by Dave

Calculus
Use a Riemann sum with n = 3 terms and the right endpoint rule to approx. ∫(1, 2) sin(1/x)dx. My teacher just needs the terms written out, no need to add or multiply. This is a problem she did up on the board, so here's her answer: sin(4/3)(1/3) + sin(5/3)(1/3) + sin...
Wednesday, November 4, 2015 by Justin

Calculus
For a cylinder with a surface area of 90, what is the maximum volume that it can have? Round your answer to the nearest 4 decimal places. The volume of a cylinder is πr^2*h and the surface area is 2πrh+2πr^2.
Wednesday, November 4, 2015 by John

Calculus
A rectangular recreational field needs to be built outside of a gymnasium. Three walls of fencing are needed and the fourth wall is to be a wall of the gymnasium itself. The ideal area for such a field is exactly 250000ft2. In order to minimize costs, it is necessary to ...
Wednesday, November 4, 2015 by Erik

HELP CALCULUS HOMEWORK DUE TODAY
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (x) / (x^2 − x + 25), [0, 15]?
Wednesday, November 4, 2015 by Anonymous

Calculus I
a). Find the critical points of the following functions on the domain or on the given interval. b). Use a graphing utility to determine whether each critical point corresponds to a local minimum, local maximum, or neither f(x)= x- tan^-1 x
Wednesday, November 4, 2015 by Mjeed

Calculus 1
a power station needs to supply power lines to a location 10 miles downstream and on the other side of a river that is 0.75 miles wide. Power lines cost $7 per foot on land and $10 per foot under water. What is the most economical path? What is the minimum cost? I know I have ...
Tuesday, November 3, 2015 by chelz

Calculus
Find the limit as x->infinity of (1+8/x)^x
Tuesday, November 3, 2015 by Callie

Pre-Calculus
You are taking a flight from Daytona Beach to St. Louis. There is a stopover in Atlanta. The bearing from Daytona Beach to Atlanta is N 38.3 degrees W. The bearing from Dayton directly to St. Louis is N 43.4 degrees W. The distance of the first leg of the trip from Daytona to ...
Tuesday, November 3, 2015 by Darshini

Calculus
Find an equation of the tangent line to the curve at the point (1, 1/e). y = (x^3)(e^−x)
Tuesday, November 3, 2015 by Callie

Calculus
Problem 5. Protein Concentration in Cells Consider a growing bacterial cell that is producing a protein involved in binary fission. Suppose that, at a particular point in time, a bacterial cell has a volume of 1000 μm3 (microns cubed) and is growing at a rate of 5 μ...
Tuesday, November 3, 2015 by Sky

Business Calculus
Bill wants to fence in his rectangular garden so his precious produce will be protected. Three sides of the fence will be constructed with wire at $2 per linear foot and the fourth side will be constructed of wood fencing at a cost of 6$ per linear foot.If he has $400 to spend...
Monday, November 2, 2015 by Rae

calculus
The edge of a cube office is decreasing at a constant rate of two cm per seconds .find the rate of change of its volume at that instant when the volume is 64m cube
Monday, November 2, 2015 by angela

Calculus 1
You have 4L feet of fence to make a rectangular vegetable garden alongside the wall of your house, where L is a positive constant. The wall of the house bounds one side of the vegetable garden. What is the largest possible area for the vegetable garden?
Sunday, November 1, 2015 by Grant

Calculus 1
A family wants to fence a rectangular play area alongside the wall of their house. The wall of their house bounds one side of the play area. If they want the play area to be exactly 1600ft^2, what is the least amount of fencing needed to make this? Round your answer to the ...
Sunday, November 1, 2015 by Grant

Calculus
Use the Shell Method to compute the volume V of the solid obtained by rotating the region enclosed by the graphs of the functions y = x^2, y = 8 − x^2,and x = 1/2 about the y-axis. Here is how I set up the integral: 2 pi integral sign [-2,2] (1/2 - x)[(8-x^2)- (x^2)]dx ...
Saturday, October 31, 2015 by Anonymous

Calculus
The volume V of a growing spherical cell is V =4/3πr^3, where the radius is measured in micrometers (1 µm = 10^−6m). Find the average rate of change of V with respect to r when r changes from 3 to each of the following. i)3 to 6µm ii)3 to 4µm
Saturday, October 31, 2015 by Joey

Pre calculus
A plane is headed due south with an airspeed of 190 mph. A wind from the direction of S 40 degrees W is blowing at 30 mph. Find the groundspeed of the plane, rounded to the nearest whole number
Friday, October 30, 2015 by Jacob

Calculus 1
Consider the following. B(x) = 3x^(2/3) − x (a) Find the interval of increase.(Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local maximum value(s).(Enter your answers as a comma-...
Friday, October 30, 2015 by TayB

Calculus 1
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (e^−x)*(− e^−6x), [0, 1]
Friday, October 30, 2015 by TayB

Calculus 1
Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=(x^2-4)/(x^2+4), [-4,4]
Thursday, October 29, 2015 by TayB

Pre-Calculus
Use the CALC features of the TI to answer the following. Show what you put into the calculator & what CALC feature you used. Round to the nearest tenths. The equation h = 20 cos (π/4 (t-3)) + 23 tells how high above the ground a ferris wheel car is at any given time. h is...
Thursday, October 29, 2015 by Clarice

calculus
why is sec(pi)x = (1/pi)secx
Thursday, October 29, 2015 by Marcelo

Pre-calculus
A surveyor standing 62 meters from the base of a building measures the angle to the top of the building and finds it to be 38°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 45°. How tall is the tadio tower?
Thursday, October 29, 2015 by Fred

AP CALCULUS HELP
first, we must find 2z(dz/dt)=2x(dx/dt) + 2y(2y/dt) simplifying, we get: dy/dt=???(dx/dt + dy/dt) What is that simplified?
Wednesday, October 28, 2015 by Anonymous

Calculus
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.02 cm thick to a sphere with diameter 40 meters. (Recall that the volume of a sphere of radius r is V=(4/3)πr^3. Notice that you are given that dr=0.02.)
Wednesday, October 28, 2015 by Henry

Pre-Calculus
During a storm a ship is being tossed up and down by huge waves. The vertical motion of the ship is given by the equation: h = 21cos((2π/5)t) where h is height above sea level in feet at time t minutes. 1) Give the first 2 times that the ship is at sea level. 2) Give a ...
Wednesday, October 28, 2015 by Clarice

Calculus
The consumer demand equation for tissues is given by q = (97 − p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E when the price is set at $26. (Round your answer to three decimal places.) E =...
Wednesday, October 28, 2015 by Megan

Calculus - Differentiate
Differentiate y= (sin(x)) / (x^4) y' = ?
Wednesday, October 28, 2015 by victoria

Calculus
Let f(x)=x^4. If a=1 and dx=Δx=1/2, what are Δy and dy?
Wednesday, October 28, 2015 by Henry

Calculus
The formula for the amount (A) in a savings account compounded n times per year for t years at an annual interest rate r, with initial deposit P, is given by A=P(1+r/n)^nt. Evaluate this formula as the number of compoundings per year becomes infinite. (the number "e"...
Tuesday, October 27, 2015 by Nick

Calculus
A baseball player hits a baseball from home base towards second base with a velocity of 90 feet/second. At that same moment, he runs from home base towards first base at 30 feet/second. Find the rate of change of the distance between him and the baseball after 1 second.
Tuesday, October 27, 2015 by Nick

Pre-Calculus
3. Joyce is buying a pair of jeans for $39.99. The jeans are on sale at a 20% discount and the sales tax is 7%. Write a function T(x) to represent the total cost of an item with 7% sales tax. Find the composite function (T of S)(x).Use the composition to find the final cost of...
Tuesday, October 27, 2015 by PLEASE HELP

calculus
using the squeeze theorem, find the limit as x->0 of x*e^[8sin(1/x)] what i did was: -1<=sin(1/x)<=1 -8<=8*sin(1/x)<=8 e^(-8)<=e^[8*sin(1/x)]<=e^(8) x*e^(-8)<=x*e^[8*sin(1/x)]<=x*e^(8​) lim x->0 [x*e^(-8)] = 0 lim x->0 [x*e^(8)] = 0 hence...
Tuesday, October 27, 2015 by Lid

CALCULUS TEST TOMORROW
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1 R = 1 R1 + 1 R2 . If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast ...
Monday, October 26, 2015 by Anonymous

Calculus
Let R be the interior of the circle 4x2 + 4y2 −4x = 0. Evaluate double integral sqrt(x^2+y^2)
Monday, October 26, 2015 by Calculus 3

COLLEGE CALCULUS HELP
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1 R = 1 R1 + 1 R2 . If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast ...
Monday, October 26, 2015 by Anonymous

Calculus
A force of 6 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.6 feet beyond its natural length? could you please explain how. thanks
Monday, October 26, 2015 by john

Calculus plz help integral
Find the integral of §x^1/2.e^xdx at upper limit of 1/2 and lower limit of zero..show work plz
Monday, October 26, 2015 by Collins

Calculus help
Solve using implicit derivative cuberoot(x)+cuberoot(xy)=4y^2
Monday, October 26, 2015 by Collins

Calculus
What is the maximum volume of a closed box with a square base which can be made by bending the material? The box is to have a surface area of 100in^2.
Sunday, October 25, 2015 by Paige

Calculus
You need to do the fencing of two side by side areas with 102 meters of wood fencing. What is the maximum area that you will be able to enclose?
Sunday, October 25, 2015 by Taylor

Calculus
Hello, Tutors! I am struggling on how to do problems related to finding the volume using integrals. Could you please help me? Any easy-to understand resources? Thank You for all your help. I am thankful for you tutors!!!!!!!
Sunday, October 25, 2015 by Anonymous

Calculus
1. Calculate the population within a 7-mile radius of the city center if the radial population density is ρ(r) = 5(5 + r2)1/3 (in thousands per square mile). (Round your answer to two decimal places.) 2. A population of insects increases at a rate 280 + 8t + 1.5t2 insects...
Sunday, October 25, 2015 by Anonymous

Calculus
What is the average value of f(x) on [0,4] if the area between the graph of f (x) and the x-axis is equal to 12? I used the average value formula and got 12. But the answer key says 3. My work: M= 1/4 [12x] interval: [0,4] 48/4=12
Sunday, October 25, 2015 by Tiffany

Calculus help plz
Using the first rule of derivative find 8(x-y)12?? And how can i solve these y^x+x^y=17,x+y=5
Saturday, October 24, 2015 by Franklin:

Calculus 1
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = sqrt(x), [0,16]
Saturday, October 24, 2015 by TayB

Calculus 1
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = x^3−x^2−20x + 7, [0, 5]
Saturday, October 24, 2015 by TayB

Calculus 1
find the critical numbers of the function F(x)=x^(4/5)(x-1)^2
Friday, October 23, 2015 by TayB

Calculus-Steve
Find the area of the region between the graphs of f(x)=3x+8 and g(x)=x^2 + 2x+2 over [0,2]. I got 34/3. Calculus - Steve ∫[0,2] (x^2+2x+2) dx = 1/3 x^3 + x^2 + 2x [0,2] = 8/3 + 4 + 4 = 32/3 Why are you taking the antiderivative of x^2 +2x+2 when we are trying to find the...
Thursday, October 22, 2015 by Tiffany

Calculus
Find the area of the region between the graphs of f(x)=3x+8 and g(x)=x^2 + 2x+2 over [0,2]. I got 34/3.
Thursday, October 22, 2015 by Tiffany

Calculus III
What is the velocity vector of a particle traveling to the right along the hyperbola y=x−1 with constant speed 1 when the particle's location is (4, 14). (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list of i, j ...
Thursday, October 22, 2015 by Kevin

Calculus III
Compute the length of the curve r(t)=5ti+8tj+(t2+4)k over the interval 0≤t≤6 Hint: use the formula ∫t2+a2‾‾‾‾​‾‾‾√dt=12tt2+a2&​#8254;‾‾‾‾‾​;‾√+12a2ln(t+...
Thursday, October 22, 2015 by Steven

Calculus
A long rectangle sheet of metal, 15 inches wide is to be made into a rain gutter by turning up equal amounts on each side so that they are perpendicular to the sheet. How many inches should be turned up in order to give the gutter its greatest capacity (i.e. maximize the ...
Thursday, October 22, 2015 by Gaston College

Related Rates Calculus
A man 1.8 m tall is walking at a rate of 1.5 m/s away from a streetlight. It is found that the length of his shadow is increasing at a rate of 0.9 m/s. How high above the ground is the streetlight?
Wednesday, October 21, 2015 by Sisi

Calculus i need help plz plz
Integrate:Sinxcosx/a^2cos^2(x)+b^2sin^2(​x))dx??? plz i need the full working too hard for me
Wednesday, October 21, 2015 by Collins

Calculus
A graphic designer is asked to create a movie poster with a 128 in^2 photo surrounded by a 4 in border at the top and bottoms and a 2 in border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?
Wednesday, October 21, 2015 by Anonymous

Calculus 1
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer values. If an answer does not exist, enter DNE.) f(θ) = 4 cos θ + 2 sin^2 θ
Wednesday, October 21, 2015 by TayB

Calculus 1
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^(5)e^(-6x)
Wednesday, October 21, 2015 by TayB

Calculus 1
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) F(x) = x^4/5(x − 1)^2
Wednesday, October 21, 2015 by TayB

Calculus 1
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(t) = t^(3/4) − 3t^(1/4)
Wednesday, October 21, 2015 by TayB

Calculus
Estimate the relative rate of change of f(t)=5t^2 at t=4. Use change of 0.01.
Tuesday, October 20, 2015 by Julie

Math 142 (calculus)
Determine d^2y/dx^2 for y=(5x^5+7)^4
Tuesday, October 20, 2015 by Matt

Calculus
Find constants a and b in the function ax^b/ln(x) such that f(1/5)=1 and there is a local min at x=1/5
Tuesday, October 20, 2015 by Tanner

Pre-calculus
(y-7)^2 = 12x Find the directrix
Tuesday, October 20, 2015 by Cope

Calculus...need help
Prove that the integral 1/root(ax^2+bx+c)dx=1/root(a)|n(2ax+b+2r​oot(a(ax^2+bx+c)]+k....please i don,t no it
Tuesday, October 20, 2015 by Collins

Calculus 1
Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) = 6 cos t, −3π/2 ≤ t ≤ 3π/2
Tuesday, October 20, 2015 by TayB

Calculus 1
Find the derivative dy/dx for the following. Simplify your answer. y=(ln(x^2))/(x^3) I got (2/x x^3-3x^2 ln(x^2))/((x^3)^2) for the derivative is that correct? Or no?
Tuesday, October 20, 2015 by TayB

Calculus
If the velocity function of an object is v(t) = -5t4 - 20t + 100, find the displacement function given that the displacement is 50 ft when time is 1 second
Monday, October 19, 2015 by Chong

Pre-calculus
Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter a.) x-3y+2z=21 5x-13y+12z=81 I have an answer but i'm not sure if it's ...
Monday, October 19, 2015 by Sarah

Calculus
What is the shortest distance from the surface xy+6x+z^2=33 to the origin?
Sunday, October 18, 2015 by A

Calculus
A company manufactures x units of one item and y units of another. The total cost in dollars, C, of producing these two items is approximated by the function C=7x^2+xy+1y^2+600. A) If the production quota for the total number of items (both types combined) is 182, find the ...
Sunday, October 18, 2015 by A

Pre Calculus
A park has a circular walking path with a diameter of 250 meters. a) Write the equation to describe the walking path in your diagram. b) Find the distance traveled by someone walking once around the entire path. c) Find the distance traveled by someone walking counterclockwise...
Sunday, October 18, 2015 by Erika G.

Calculus i need help plz plz
If y=ws^3/d^4 find the % increase in 'y' when 'w' increases by 2% and 's' decreases by 3% and 'd' increasee by 1%...... There a little error in the first question i post here it is plz i need the working and explanation
Sunday, October 18, 2015 by Collins

Calculus
How do I calculate the following? tan−1(tan(8)) − tan−1(tan(4))
Sunday, October 18, 2015 by Anonymous

HELP CALCULUS
Find dy/dx by implicit differentiation. tan−1(4x2y) = x + 3xy2
Saturday, October 17, 2015 by Anonymous

calculus
solve the differential equation that satisfies the given condition: dy/dx=(ycos(x))/(6+y^2), y(0)=1
Saturday, October 17, 2015 by Lauren

Calculus
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (0,1) where f'(c)=0. f(x) = x3 - 2x2 + x, [0, 1] Round your answer to two decimal places.
Saturday, October 17, 2015 by olga

Calculus
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (-3, -2) where f'(c)=0. f(x) = x + 6x-1 , [-3, -2] Round your answer to two decimal places.
Saturday, October 17, 2015 by olga

Calculus
The function defined below satisfies the Mean Value Theorem on the given interval. Find the value of c in the interval (1, 2) where f'(c)=(f(b) - f(a))/(b - a). f(x) = 1.5x-1 + 1.1 , [1, 2] Round your answer to two decimal places.
Saturday, October 17, 2015 by olga

Calculus
Determine the linear approximation of 21/2. Express your answer as a reduced fraction in the form a/b.
Saturday, October 17, 2015 by olga

Calculus
The measurement of the side of a square is found to be 12 cm with a possible error of 0.05 cm. Use differentials to estimate the propagated error ΔA in computing the area of the square. Please do not include the ± symbol in your answer. Round your final answer to ...
Saturday, October 17, 2015 by olga

Calculus
Which of the following is the linear approximation formula, L(x), that estimates values of y = ln(x) + 1 for values of x near 1? a) y = x - 1 b)y = x c)y = x + 1 d)y = -x
Saturday, October 17, 2015 by olga

Calculus also need help plz plz plz
If z=1/(x^2+y^2-1) is x(dz/dx)+y(dz/dy)=-2z(1+z) or -z^2(1+z) note:dz/dx=partial derivative of x and dz/dy=partial derivative of y??
Saturday, October 17, 2015 by Collins

Calculus badly need help so difficult
If y=ws^3/d^4 find the percent increase in y when w increase by 2% s decrease by 3% and s decrease by 1% plz show the full solution the question is byond my power
Saturday, October 17, 2015 by Collins

Calculus
Find c so y=4x+3 is tangent to the curve y=x^2+c
Friday, October 16, 2015 by Matt

Calculus
An open box with a capacity of 36,000 cubic inches is to be twice as long as it is wide. The material for the box is $.10/sq ft. What are the dimensions of the least expensive box? How much does it cost?
Friday, October 16, 2015 by Matt

Calculus
An open box is made by cutting squares of side w inches from the four corners of a sheet of cardboard that is 24" x 32" and then folding up the sides. What should w be to maximize volume of the box? I started by trying to get a formula for the volume which I thought ...
Friday, October 16, 2015 by Matt

Pre-Calculus
The angle of depression from the top of a 75 ft. lighthouse to a ship out in the ocean is 40*. How far out is the ship from the lighthouse? I've been stuck on this problem for an hour, I know the answer but don't know how to set it up/enter it in a calculator.
Thursday, October 15, 2015 by Jason

Integral Calculus
Initial Value Problem dy/dx = y^2 -5y+6 y(0)=1
Thursday, October 15, 2015 by Chintu

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Homework Help: Math