# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**Calculus**

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes.

**Calculus**

A spherical balloon is being inflated and the radius is increasing at a constant rate of 2 cm per minute. At what rates are the volume and surface area of the balloon increasing when the radius is 5 cm? For this problem do I plug in the 5 cm into the Volume formula ( 4/3 pi r^...

**Calculus**

Two cars leave an intersection at the same time. Car X is travelling East at 50 km/hr and Car Y is travelling South at 60 km/hr. Find the rate at which the cars are separating after 30 minutes.

**Calculus**

two small planes take off from the same airport at the same time. One travels north at 200 km/h, and the other, west at 150 km/h. If the planes fly at the same altitude, how fast are they separating after 2 hours?

**Calculus**

A boat is held at a dock by a bow line which is wound about a circular windlass 3 feet higher than the bow of the boat. How fast is the bow line increasing its length at the instant the boat is 4 feet from the dock if the boat is drifting at a rate of 7 feet per second from ...

**CALCULUS**

Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the ...

**AP Calculus**

A race car is running practice laps in preparation for an upcoming race. To judge how the car is performing, the crew takes measurements of the car's speed S(t) (in miles per hour, or mph) every minute. The measurements are given in the table below. t (min) --- S(t) (mph 0...

**Calculus**

An equation of the line with slope -1 that passes through the point (2,5) is y=-x+7

**Calculus quick question pls**

Why is there no vertical asymptote on F(x) = x/(x^2+1) What i learned is that to find vertical asymptote you have to set the denominator To 0 and solve for x ? In that case I find that x=-1,1

**calculus**

Find the maximum value of the function f(x)=(x^2+9x-3) / x^2

**calculus**

Find the critical numbers for the function f(x) = 2x / sqrt(x-1)

**Calculus**

a(t)=4sin3t;v(0)=1,s(0)=6 I'm trying to find expression for s(t). Should I wait till the end to add find and add constant. I got [1/9(13t-4sin(3t))+6] and it was wrong.

**Calculus!!**

Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)? Justify your answer. B. Find the particular...

**AP Calculus**

Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0. A. Does f have an inflection point at x=0? Explain your answer. B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g. Write the equation of...

**Calculus**

Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the ...

**Calculus**

Let M be the region under the graph of f(x) = 3/e^x from x=0 to x=5. A. Find the area of M. B. Find the value of c so that the line x=c divides the region M into two pieces with equal area. C. M is the base of a solid whose cross sections are semicircles whose diameter lies in...

**Calculus**

A race car is running practice laps in preparation for an upcoming race. To judge how the car is performing, the crew takes measurements of the car's speed S(t) (in miles per hour, or mph) every minute. The measurements are given in the table below. t (min) --- S(t) (mph 0...

**AP Calculus**

Consider a curve given implicitly by the equation (1+x)y^3 + (x^4)y - 85 = 0. A. Calculate dy/dx at a general point (x,y). B. Write the equation of the tangent line to the curve at the point (3,1). C. At (3,1), y(x) is defined implicitly as a function of x. Let g(x) be the ...

**Calculus**

If f(2) = 2.5 and f'(2) = -2.5, then f(2.5) is approximately: A. 2.5 B. -2.5 C. -2 D. 2 E. 1.25

**Calculus**

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the time in years. A. If m(0)=20, write a ...

**Calculus**

The equation dy/dx = -6x^2/y gives the slope at any point on the graph of f(x). The range of f(x) is [0, infinity] and f(1) = 2. A. Find the equation of the tangent line to f(x) at the point (1,2). B. Write the function f(x). C. Determine the domain of the function f(x).

**Calculus**

Compute the curvature. r(t)=(t^2,2t^3/3) t >0 The answer is 1/2t(1+t^2)^3/2 I have tried multiple times but i cannot arrive to this answer.

**Calculus Help**

Evaluate lim x-->25 5 - square root x / x - 25 I don't get how the answer is -1/10

**Calculus I**

The area enclosed by the curve y^2 = x(2 − x) is given by what definite integral? Should I begin by square rooting both sides? Not really sure.

**Calculus I**

Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?

**Calculus I**

The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid?

**Calculus I**

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the y-axis, and the line y = 3 about the x-axis.

**Calculus**

What did I do wrong? An object is formed so that its base is the quarter circle y = sqrt(64 − x^2) in the first quadrant, and its cross sections along the x-axis are squares. What is the volume of the object? (Assume the axes are measured in centimeters.) I have already ...

**Math (Calculus)**

The function f(x)=-2x^3+10.2x^2+202.275x+0.87 is increasing on the open interval (?,?). It is decreasing on the open interval (-oo,?) and the open interval (?,+oo) The function has a local maximum at ? I used derivative -6x^2+20.4x+202.275 and find the root but it doesn't work...

**Calculus**

A closed box with square base is to be built. the bottom and the top of the box are to be made of a material costing $2/ft^2, and all four sides are to be made of a material costing $1/ft^2. what are the dimensions of the box of the greatest value that can be constructed for $12?

**Calculus**

A stone is dropped from the edge of a roof, and hits the ground with a velocity of −170 feet per second. Assume the acceleration due to gravity is -32 feet per second squared. How high (in feet) is the roof?

**Calculus (easy)**

What is the polar form of (-2-2i)?

**Calculus**

Let 𝑆 be the region (in the first quadrant) bounded by a circle 𝑥^2 + 𝑦^2 = 2, 𝑦^2 = 𝑥 and the 𝑥-axis (ii) Find the volume of the solid generated by rotating the region 𝑆 about the 𝑦-axis (c) Find the surface area...

**Calculus**

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) limit n approaches infinity of an = e^(−6/sqrt(n))

**Calculus**

Equation: Suppose that the demand of a certain item is x = -0.7 p + 20. Evaluate the elasticity at E = 8. I'm not sure what steps to take to solve this. I know that elasticity is equal to the absolute value of [(p/q) x (dp/dq)]

**Calculus**

The Riemann sum s for f(x)=4x^2, 0<=x<=1, taking the sample points to be the right endpoints is given by s=4n^2+6n+2/3n^2. True or False?

**Calculus (Urgent, please)**

Find the area of the region enclosed by the intersection of the circle x^2+y^2=4 and the parabola y=x^2. Show work

**calculus.can you help me on these as well@sir collins**

integrate sin^7xdx

**calculus very hard help**

integrate:cos^10xdx even with the previous hint a tutor here gave me i still don,t know it

**advanced calculus**

Many carnivals have a version of the double Ferris wheel. A large central arm rotates clockwise. At each end of the central arm is a Ferris wheel that rotates clockwise around the arm. Assume that the central arm has length 200 feet and rotates about its center. Also assume ...

**Calculus**

Let 𝑅 be the region bounded by the four straight lines 𝑦=𝑥, 𝑥+𝑦=4, 𝑦=𝑥−2 and 𝑥+ 𝑦 = 2. Find the surface area of the surface obtained by rotating the region 𝑅 about the 𝑥-axis for 1 ...

**Calculus I**

For what values of a and b is the line -4x+y=b tangent to the curve y=ax^3 when x=4? Can anyone give me the hint?

**Calculus I**

if f(x)=24, find f'(11)? How can i find it?

**Calculus**

Find the arc length of the curve 𝑥(𝑡)=cos𝑡+ү05;sin𝑡, 0≤𝑡≤𝜋/2 𝑦(𝑡) = sin 𝑡 − 𝑡 cos 𝑡 ^2

**Calculus**

Compute (f^-1) (2) if f(x) = 7x + 3cos(x) + 2sin(x).... We tried solving it in the form (f^-1)(a) = (1/f'(f^-1(a))... or is this a u-sub problem? We are trying to figure out whose way is right with one getting the answer as 1/2 and the other 1/10... we are getting mixed up ...

**calculus**

Find f'x given f(x)= 1/(1+(1/(1+(1/x))))

**math calculus**

Find the intervals on which the function f(x)=x²/³(10-x) is increasing and decreasing. Sketch the graph of y=f(x)and identify any local maxima and minima. Any global extrema should also be identified.

**Pre calculus**

1. Write in terms of cos and sin function. cotx*secx Show work.

**Pre calculus**

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance...

**calculus**

Between y = 2x2 + 9x − 4 and y = −x2 + 6x + 2 for x in [−2, 2]

**Calculus**

Find the volume of the solid generated by rotating the region above 𝑦 = 12 and below 𝑦 = sin 𝑥 for 0≤𝑥≤𝜋 about the 𝑦-axis for 1 complete revolution.

**calculus help**

integrate cos^10xdx.. .plz show working i really wanna learn these thanks anyway

**CALCULUS**

Sketch the graph of f(x)=1/(1+x^2)showing y-intercept, intervals where the graph increase / decrease, intervals where the graph is concave up/ down , inflexion point and stationary point

**Calculus**

Find the volume of the solid generated by rotating the region bounded by 𝑦 = 𝑒2𝑥, 𝑥-axis, 𝑦-axis and 𝑥 = ln3 about (i) the 𝑥-axis for 1 complete revolution. (ii) the 𝑦-axis for 1 complete revolution. (iii) &#...

**Calculus (Im I Doing This Right???? Im Unsure)**

From first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x. f(x)=2x^2−6x at x = 3 f(x)=2x^2-6x f(x+h)= 2(x+h)^2-6(x+h) =2x^2+4xh+2h^2-6x-6h lim h-->0 f(x+h)-f(x)/h =2x^2+4xh+2h^2-6x-6h - (2x^2-6x) =4xh+2h^...

**Calculus (Im I Doing This Right???? Im Unsure)**

From first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x. f(x)=2x^2−6x at x = 3 f(x)=2x^2-6x f(x+h)= 2(x+h)^2-6(x+h) =2x^2+4xh+2h^2-6x-6h lim h-->0 f(x+h)-f(x)/h =2x^2+4xh+2h^2-6x-6h - (2x^2-6x) =4xh+2h^...

**Calculus**

From first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x. f(x)=2x^2− 6x at x = 3

**Maths- Calculus**

The region R bounded by y=e^-x and y=0 and lying to the right x=0 is rotated about the y-axis

**Calculus**

Find the volume of the solid generated by rotating the region 0<y<5-x^2 about the x-axis

**calculus**

A 5.5 foot tall woman walks at 6ft/s torward a street light that is 16.5 ft above the ground. what is the rate of change of the length of her shadow when she is 14ft from the street light? At what rate is the tip of her shadow moving? How do I get the equation for this and how...

**Calculus 1**

Find the formula for a function of the form y=bxe^(-ax) with a local maximum at (4,12)...

**Calculus I**

Find numbers a and b such that: lim (sqrt(ax+b)-9)/x =1 x->0

**calculus 1**

(Thank you for any help because I am not good at setting up word problems) What are the dimensions that will minimize the amount of material needed to manufacture a standard oil drum that is in the shape of a cylinder, with closed top and bottom. The drum must have a volume of...

**calculus 1**

Mr. Smith would like to enclose a rectangular field that has an area of 1000 square feet. What is the minimum amount of fencing he will need if he only needs to use it on 3 sides since he can use the side of the barn for the fourth side.

**Pre calculus**

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance...

**Calculus**

f(x) = 3cos(x)−cos^3(x) for 0 < x < 2π I need help finding where it increases and decreases and where it concaves up and down. The inflection points I have found are pi/2 and 3pi/2.

**Calculus**

A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft. per second,how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5ft from the wall?

**Please HELP! Calculus (Implicit functions)**

Find the inverse of the function y = (square root x) + 4x , then solve for its 1st order derivative.

**Calculus Answer Confirming Not Sure Im Right Help?**

Evaluate the lim a. lim x--> 64 (cube root x-4/x-64) (∛x-4)/(x-64) -> 0/0 so then let cube root x = u u-4/u^3-64 u-4/u^3-64 = u-4/u-4(u^2+4u+16) the u-4 cancel each other out leaving lim x->64 = 1/u^2+4u+16 1/64^2+4(64)=16 oddly i find the number to large am i ...

**Calculus Help Stuck Part 2?**

Evaluate the lim a. lim x--> 64 (cube root x-4/x-64)

**Pre calculus**

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance...

**Pre calculus**

In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance from the base of the antenna to the down point DOWN hill is 95 feet. Ignore the amount of cable needed to ...

**Calculus I**

The volume of a sphere is changing at a rate of 8pi cm/sec. What is the rate of change of its surface area when the radius is 1? (the volume of a sphere is given by V=4/3pir^3 and its surface area, by A=4pi r ^2).

**Calculus Help Stuck Part 2?**

b.Determine the lim x-->4 (x^2+x-20/8-2x) What Im stuck on is this f(4)= 4^2+4-20 / 8-2(4) f(4)= 0/0 x^2+x-20/8-2x = (x-4)(x+5)/-2(x-4) What do I do next I'm so confused ik i would eliminate the x-4 from numerator and denominator but what would i do with the -2 that belongs...

**Calculus**

Determine the following limits if it exists. a. lim x-->5 (4x/x-5)

**calculus**

Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.) A ball is thrown vertically upward from a height of 4 feet with an initial velocity of 79 feet per second. How high will the ball go? (Round your answer to two decimal places.)

**Calculus**

f(x) = (x-4)/ (x^2) I need to use interval notation to indicate where f(x) is concave up or down. Concave up is (12, inf) but I can't figure out concave down. Help!

**Calculus**

Find a cubic function f(x)=ax^3+cx^2+d that has a local maximum value of 9 at -4 and a local minimum value of 6 at 0. Find a, c, and d. I know that d = 6 but I am worked for hours trying to find a and c. Please help!!

**calculus 2**

Use Euler's method with a step size of 0.2 to estimate y(1), where y(x) is the solution of the initial value problem y' = 6x+y^2, y(0)=0. Round your final answer to 4 places, but keep more places on the intermediate steps for accuracy.

**Calculus derivatives**

Consider the equation x^2 + xy + y^2 = 1 Find all points where the tangent line is parallel to the line y = −x. Thank you for helping

**Calculus**

limit of (x*(y-1)^2*cosx)/(x^2+2(y-1)^2) as (x,y)->(0,1). By evaluating along different paths this limit often goes to 0. This does not necessarily imply that it exists. So how would i prove that it exists. Can someone please show me how i can prove using delta - epsilon ...

**Please Help ! Calculus**

Find two numbers whose sum is 42 and whose product will be at the largest possible.

**Calculus**

Determine the following limits if it exists. a. lim x-->5 (4x/x-5)

**Calculus**

Find the volume of the solid bounded below by the parabloid z = x^2 + y^2 and above by the plane 2x + z = 3

**Calculus**

An energy drink container in the shape of a right circular cylinder must have a volume of 12 fluid ounces (1 fluid ounce is approximately 1.80469 cubic inches). The cost per square inch of constructing the top and bottom is twice the cost of constructing the lateral side. Find...

**Calculus (30min before deadline help pls )**

A street light is at the top of a 16 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 3 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 36 ft away from the ...

**Calculus**

Find the largest volume V of the circular cone that can be inscribed in a sphere of radius = 10 cm

**Calculus**

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $60/ft and on the other three sides by a metal fence costing $50/ft. If the area of the garden is 102 square feet, find the dimensions of the garden that minimize the cost.

**Calculus**

Reverse the order of the double integral (y+1) dx dy, where -1<= y <= 4 and y - 4 <= x <= 4y-y^2

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.

**Calculus**

Find a cubic function f(x)=ax^3+cx^2+d that has a local maximum value of 9 at -4 and a local minimum value of 6 at 0. Find a, c, and d.

**Calculus**

Suppose the derivative of a function f is f′(x)=(x−8)^7(x−1)^4(x+19)^8. Then the function f is increasing on the interval what?

**Calculus**

Consider the function f(x)=xsqrt(36−x^2), −1≤x≤6. This function has an absolute minimum value equal to what?

**calculus**

Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.) A ball is thrown vertically upward from a height of 4 feet with an initial velocity of 79 feet per second. How high will the ball go? (Round your answer to two decimal places.)

**calculus**

The maker of an automobile advertises that it takes 15 seconds to accelerate from 15 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration, (a) The distance the car travels during the 15 seconds (Round your answer to two decimal places.)

**calculus**

Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.) A ball is thrown vertically upward from a height of 4 feet with an initial velocity of 79 feet per second. How high will the ball go? (Round your answer to two decimal places.)

**Calculus**

A festivals being planned. The planners need to enclose to adjacent 200 M^2 areas with fencing. They have budgeted $1000 for fencing. Fencing currently cost $10/meter. The diagram of the area is as follows: (The diagram is 2 adjacent squares, the areas of both squares are 200 ...

**calculus**

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'(t) is its velocity, and x''(t) is its acceleration. A particle moves along the x-axis at a velocity of v(t) = 5/√t, t > 0. At time t = 1, its position is x = 11. Find ...

**calculus**

Use a(t) = −9.8 meters per second per second as the acceleration due to gravity. (Neglect air resistance.) A canyon is 2300 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds...

**calculus**

Use a(t) = -9.8 meters per second per second as the acceleration due to gravity. (Neglect air resistance.) A baseball is thrown upward from a height of 3 meters with an initial velocity of 7 meters per second. Determine its maximum height. (Round your answer to two decimal ...