# Calculus

**Calculus**

Find the equation of the line that is tangent to the curve x(t) = t^2+1 and y(t)=t^3-1 at the point (5,7). I get a slope of 7.5.

**Calculus**

a stone is thrown into a pond creating ripples that are concentric circles. the rate of change of the radius of the circle is 3 ft/min. if the radius is 0 at the time=0, how fast is the area increasing after 4 minutes

**Calculus**

What is the equation of the line which passes through the point (6,4) and is parallel to the line with the parametric equations x=5t+4 and y=t-7? I think the answer is y = 1/5x + 14/5.

**Calculus**

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. g(x) = 2x^2 − x − 1, [3, 5], 4 rectangles __ < Area < __

**Calculus**

A uniform layer of ice covers a spherical water-storage tank. As the ice melts, the volume V of ice decreases at a rate that varies directly as the surface area A. Show that the outside radius decreases at a constant rate.

**Calculus**

Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -3 I got the integral from 1 to 2.718 of pi(1)^2-pi(ln(x))^2 Is this correct or is there a trick I'm missing ...

**Calculus - derivatives of e**

Find an equation of the tangent line to the graph of y = e^(−x^2) at the point (5, 1/(e^25)). My work: y' = -2xe^(-x^2) y' when x = 5 = -10e^25 y - (1/e^25) = -10e^25 * (x - 5) y = (-10e^25) (x - 5) + (1/e^25) This is incorrect. How?

**Grade 12 Calculus**

A science project studying catapults sent a projectile into the air with an initial velocity of 24.5 m/s. The formula for distance (s) in meters with respect to time in seconds is s = -4.9t2 + 24.5t. a)Find the time that this projectile would appear to have the maximum ...

**Calculus**

Find the first three non-zero terms and the general term for the power series representation of f(x) = 1/(x^2 + 3). I came up with 1/3 - x^2/9 + x^4/27, but I don't know the general term.

**Calculus**

Determine how many terms are required to approximate the sum of the series ((-1)^(n+1))/n^2 from n = 1 to inf with an error of less than 0.001.

**Calculus**

Find the first three nonzero terms and the general term of the Maclaurin series generated by e^(-6x). My answer: 1 + x + (x^2)/2, general term (x^(n-1))/(n-1)!

**Calculus**

what is the integral to find the volume of the solid that is formed when the region bounded by the graphs of y = e^x, x = 2, and y = 1 is revolved around the line y = -1. I got pi[integral from 0 to 2] e^2x-1^2 dx. I'm not sure about the 1^2 though because that function is in ...

**Calculus**

Determine the number of terms required to approximate the sum of the series from n=1 to infinity of ((-1)^(n+1))/(2n^3 - 1) with an error less than 0.001. I think this is 5 terms, but I'm unsure whether to set this up as 2n^3 - 1 < 0.001 or 2(n + 1)^3 - 1 < 0.001.

**Calculus**

Sarah is filling ice cream cones with shaving cream to hand out to trick or treaters. The cones have a largest radius of 3 centimeters and a depth of 13 centimeters. She fills them at a rate of 5 cubic centimeters per second. (She works carefully so that shaving cream is ...

**Calculus**

How would you find the radius of convergence when you end up with something like |8x - 1| < 1? Do I divide everything by 8 and get a radius of 1/8?

**Calculus**

Find the area of the region bounded by the curves y = x^2 - 1 and y = cos(x). I've tried doing this and I got -1.54 which doesn't make sense because area should always be positive right? And I put it in an online calculator to check and it gave me 3.11. I think I may have ...

**Calculus**

Hello, I would like to know if you can help me with this problem the intergal of (cos (6x)+1), I’ve understood it as far as cos (1/2 (ax)) but where is the sqrt of 2 coming from?! Thank you.

**Calculus**

Find the radius of convergence of the series from n=0 to infinity of ((9x-4)^(2n+1))/(n^(3/2)). I think it is 5/9.

**Calculus**

Find how many terms are required to approximate the sum of the series from 1 to infinity of (-1)^(n+1)/(n^3) with an error of less than 0.001. I think 11 terms are required.

**calculus**

Find the value of $800 deposited in a bank at 10% interest for 8 years compounded in the following ways. (Round your answers to the nearest cent.) (a) annually_________$ (b) quarterly_________$ (c) continuously________$

**Calculus**

The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population, P, of the rats is expected to grow according to the differential equation dP/dt equals the product of 0.04 times P and the quantity 1 minus P over ...

**calculus**

The reproduction function for a sardine is f(p) = −0.0004p^2+3p, where p and f(p) are in hundred metric tons. Find the population that gives the maximum sustainable yield, and the size of the yield. population=_________ hundred metric tons size of yield=__________ hundred ...

**calculus**

Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p^2 + 8p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.

**Calculus**

The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in miles per hour. T = 2.5x + 0.5x^2 Approximate the change and percent change in total stopping distance as speed changes from x = 15 to x = 18 miles per hour. (Round your answers...

**Calculus**

Use the information to evaluate and compare Δy and dy. (Round your answers to three decimal places.) y = x4 x = 1 Δx = dx = 0.1 I'm totally lost

**Calculus**

Determine whether the series from 0 to infinity of cos(nπ)/(n + 3) converges conditionally or absolutely. A. The series diverges. B. The series converges conditionally but not absolutely. C. The series converges absolutely but not conditionally. D. The series converges ...

**Calculus**

A rectangular page is to contain 97 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

**Calculus**

A girls throws a tennis ball straight into the air with a velocity of 64 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves the girl's hand will it take the ball to reach its highest point? Assume the position at time t = 0 is 0 feet. Ok ...

**Calculus**

An underwater viewing window is installed at an aquarium. The window is circular with radius 5 feet. The center of the window is 40 feet below the surface of the water. Find the hydrostatic force on the window.

**Calculus**

The base of a solid in the region bounded by the graphs of y = e^-x, y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid? Answers: 1)(pi/16)e^2 2)(pi/16)(1-1/e^2) 3)(pi/4)(1-1/e^...

**AP Calculus**

Find x. lim (sin(x))^x x-->0

**Calculus**

Use the ratio test to find whether the series diverges or converges. 1/5^n (1 to infinity) I think the limit converges to 1/5, so the series converges.

**Calculus**

For the series from 1 to inf of (2n^2 - 1)/(3n^5 + 2n + 1), would it be possible to compare (2n^2 - 1)/(3n^5 + 2n + 1) to 2/3^3 for the limit comparison test?

**Calculus**

Which integral represents the limit as x approaches inf. of 1/n(√(1/n) + √(2/n) + ... √(n/n))? A. int from 0 to 1 of x dx B. int from 0 to 1 of √x dx C. 1/2 * int from 0 to 1 of 1/√x dx D. 2 * int from 1 to 2 of x√x dx

**Calculus**

For what values of x does the series 1 + 2^x + 3^x + 4^x + ... + n^x + ... converge? A. No values of x B. x >= -1 C. x > -1 D. x < -1 E. All values of x I think the answer is C, because n^(-1) = 1/n, which diverges.

**Calculus 2**

Calculate the arc length of y= 1/4x^2−1/2ln(x) over the interval [1,6e]

**Calculus 2**

Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(X), y=0, x=0, x=pi/2 about the line y=-1 Volume=?

**Calculus 2**

The region between the graphs of y=x^2 and y=6x is rotated around the line x=8. The volume of the resulting solid is?

**Calculus**

How do I figure out if the series from 3 to inf of ((1/2)^(n+1))((2/3)^n) converges or diverges? I think it has something to do with the value of r, but this problem is confusing me because it is written as a product.

**Calculus (increasing/decreasing)**

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If the answer cannot be expressed as an interval, enter EMPTY or ∅.) f(x) = (5 − x^2) / x my work: a) f'(x)=(-x^2-5)/x^2 b) set ...

**Calculus**

Determine whether the sequence (-1)^n(n/(n+1)) diverges or converges. I think it diverges because the limit as n approaches inf. of n/(n+1) is 1, and the limit of (-1)^n does not exist.

**Calculus**

Can someone check my work and answer? Evaluate the integral from -1 to 0 of (4x^6+2x)^3(12x^5+1)dx My work: let u=4x^6+2x dx=du/24x^5+2 now we have the integral from -1 to 0 of u^3(12x^5+1)(du/24x^5+2) Simplifies to the integral from -1 to 0 of u^3(1/2+1/2) simplifies to the ...

**calculus**

Find the interval on which the curve of y= the integral from 0 to x of 2/(1+3t+t^2)dt is concave up. I asked this question yesterday and I would like to see if someone could check my answer. I got the curve is concave up when x<-1.5

**Calculus**

a small business estimates that its profit from producing x items can be modelled by: P(x) = 0.003x^3 - 1.5x^2 + 200 - 1000 due to limited space and capital, the number of items produced must not exceed 350 items. Explore the model and make suggestions to the business owner to...

**calculus**

Find the interval on which the curve of y= the integral from 0 to x of 2/(1+3t+t^2)dt is concave up. Can someone please explain? I'm so confused about how to find the answer, all I know is if the 2nd derivative is positive then it's concave up.

**calculus**

The total cost (in dollars) of producing x college textbooks is C(x) = 50x+ 11,000 What is the fixed cost? 11,000 What is the marginal cost? What is the total cost of producing 700 books? 34,000 books? What is the average cost when 700 books are produced? When 34,000 books are...

**Calculus 2**

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=0, x=1 and x=4 about the line y=−1

**Calculus 2**

Find the volume of the solid whose base is the semicircle y= sqrt(1− x^2) where −1≤x≤1, and the cross sections perpendicular to the x -axis are squares.

**Calculus**

Your classmate claims that the the function f(x,y) = x^3(e^{x^2−3y^2})−(17−3x^2)(y−2) does not have an absolute maximum nor an absolute minimum when the function is restricted to the disk x^2+y^2 ≤ 7. Please explain why this is incorrect.

**Math calculus 2**

Find the volume of the solid generated by revolving the given region about the line x=16: y=4-x,y=0,y=2,x=0.

**Math calculus 2**

Let S be the region of the xy-plane bounded above by the curve ((x^3)*y)=64, below by the line y=1, on the left by the line x=2, and on the right by the line x=4. Find the volume of the solid obtained by rotating S around (a) the x axis (b) the y axis (c) the line x=2

**Math calculus 2**

Find the volume of the solid generated by revolving the region enclosed by the curves y=5*(sqrt(x)), y=0, and x=2 about the line x=9.

**Math calculus 2**

A propane tank is in the shape generated by revolving the region enclosed by the right half of the graph of (4*x^2)+(64*y^2)=144 and the y-axis about the y-axis. If x and y are measured in meters find the depth of the propane in the tank when it is filled to one-quarter of the...

**Calculus**

Which of the following series converge? A. ∑n=1 to infinity of 1/n^2 B. ∑n=1 to infinity of 1/n C. ∑n=1 to infinity (-1)^n/(√n) I think the answer is A and C.

**Calculus Please Help**

How much work is required to lift a 700kg satellite to an altitude of 1x10^6m above the surface of the earth? The gravitation force is F=GMm/r^2, where M is the mass of the earth, m is the mass of the satellite, and r is the distance between them. The radius of the earth is 6....

**Calculus**

For what values of k does the series ∑n=1 to infinity (11/(2k^2 + 3))^n converge? I think this is k < -2 and k > 2.

**Calculus**

Which of the following series converge? A. 1 + 1/2^2 + 1/3^2 + ... + 1/n^2 + ... B. 1 + 1/2 + 1/3 + ... + 1/n + ... C. 1 - 1/3 + 1/3^2 - ... + ((-1)^(n+1))/(3^(n-1)) + ... I think A and C are the answer.

**Calculus**

For what value of the constant c is the function f continuous on (âˆ’âˆž, âˆž)? f(x) = cx2 + 4x if x < 3 x3 âˆ’ cx if x â‰¥ 3

**Pre-Calculus**

How is the function f(x)=-1/2sin5x related to the function g(x)=4sin5x?

**Calculus**

Find if the sequence an = 5/(n+2) diverges or converges. I think it diverges because the limit as x approaches infinity does not exist.

**pre-calculus**

A pilot wishes to fly on course 290 with an air speed of 300 knots when the wind blows from 224 at 18 knots. Find the drift angle to the nearest hundredth of a degree.

**Math calculus 2**

Find the volume of the solid obtained by revolving the region bounded by y=22*x−22*(x^2) and the x-axis around the x-axis.

**Calculus**

Find all points of intersection (r,theta) of the curves r=4cos(theta), r=1sin(theta). Next find the area inclosed in the intersection of the two graphs.

**Calculus**

What do you think the appropriate limit is of this sequence? 0.7, 0.72, 0.727, 0.7272,... The answer my textbook gives is 27/99. I have no idea how they got that answer. How do I solve this question?

**Calculus**

Let (a, b) be any point on the graph of Prove that the area of the triangle formed by the tangent through (a, b) and the coordinate axes is 2. This is the solution from the solution manual The coordinates of the point are (a,1/a). The slope of the tangent is -1/a^2. The ...

**Calculus**

I have no idea how to do this, can someone please help? Consider the graphs below, which give m(x) in the left graph, in black, and n(x) in the right graph, in blue. Both functions have a sharp corner at x=50. Let h(x)=n(m(x)). Find a point x where h'(x)=1.44 x= 40< m(x) &...

**Calculus**

I have no idea how to do this, can someone please help? Consider the graphs below, which give m(x) in the left graph, in black, and n(x) in the right graph, in blue. Both functions have a sharp corner at x=50. Let h(x)=n(m(x)). Find a point x where h'(x)=1.44 x= 40< m(x) &...

**Calculus**

I have no idea how to do this, can someone please help? Consider the graphs below, which give m(x) in the left graph, in black, and n(x) in the right graph, in blue. Both functions have a sharp corner at x=50. Let h(x)=n(m(x)). Find a point x where h'(x)=1.44 x= 40< m(x) &...

**calculus**

Estimate the area under the curve f(x) = x2 from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer.

**Calculus 2 (math)**

A factory installs new machinery that will save 1250−38x dollars per year, where x is the number of years since installation. However, the cost of maintaining the new machinery is 81x dollars per year. Find the accumulated savings that will occur before the machinery should ...

**math calculus 2**

Find the area of the region RR bounded by y=sin(x), y=cos(x), x=−π/3, x=13/6.

**Math calculus 2**

The revenue, in millions of dollars, for a company in year t is given by the function: R(t)=15*e^(0.08*t), 0≤t≤15 and the cost, in millions of dollars, to run the company in year t is approximated by: C(t)=12*e^(−0.04*t), 0≤t≤15 where t is the number of years after ...

**Calculus**

How do I take the indefinite integral of (5-x)/(2x^2+x-1)? I've tried splitting it into two integrals and even completing the square on the bottom but neither of those led me anywhere. Help?

**AP Calculus AB**

Suppose f(x)= x^5 - 10 and let h(x) be the inverse of f. Find h'(22).

**calculus**

Express the following as a product containing only sines and/or cosines. sin9x−sin7x

**calculus**

Find all solutions in the interval [0,2π) sin3x−sinx=0

**Math calculus 2**

Find the integrating factor for the following differential equation (cos8x)yâ€²+8(tan8x)y=4sec8x,0<x<Ï€/16.

**Math calculus 2**

A 17650 cubic foot room initially has a radon level of 870 picocuries per cubic foot. A ventilation system is installed that brings in 385 cubic feet of air per hour that contains 5 picocuries per cubic foot, while an equal quantity of the well-mixed air in the room leaves the...

**calculus**

A corporation starts to invest part of its revenue continuously at rate of P dollars per year in a fund for future expansion plans. Assume the fund earns money at an annual interest rate, r, compounded continuously. The rate of growth of the amount A in the fund is given by dA...

**Math calculus 2**

A 500-gallon tank initially contains 200 gallons of brine containing 85 pounds of dissolved salt. Brine containing 1 pounds of salt per gallon flows into the tank at the rate of 44 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 1 gallon ...

**Math calculus 2**

Pam owns an electronics store with storage capacity for 100 computer tablets. She currently has 90 computer tablets in inventory and determines that they are selling at a daily rate equal to 17% of the available capacity. When will Pam sell out of computer tablets?

**calculus**

please help! having issue with exponent part of problem. I come to 16x^4 but I think it should be 16x^3.i also have complications with finding the domains. find the derivative of the function using the definition of derivative. f(x)=4x^4 f'(x)=? State the domain of the ...

**Math (Calculus)**

The prompt for this question is f(x) =sin(x^2) A)Write the first four terms of the Maclaurin series for f(x) B)Use the Maclaurin series found in Part A to approximate the integral from 0 to 1 of sin(x^2) dx C)How many terms are needed to find the value of the integral given in...

**Math (Calculus)**

How can I sketch a graph of the first two partial sums for the following power series: Sum(n=1 to infinity) ((2x+5)^n) / (n(4^n))

**Math (Calculus)**

Consider the curve represented by the parametric equations x(t)= 2+sin(t) and y(t)=1-cos(t) when answering the following questions. A) Find Dy/Dx in terms of t I got tan(t) B) Find all values of t where the curve has a horizontal tangent. I got (+-)(pi)(n) C) Find all values ...

**Calculus (limits)**

Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2ax + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f? I. lim f(x) exists as x approaches a II. f(a) exists III. f(x) is continuous at x = a. A. None B. I, II, and III C. I ...

**Business calculus**

The RideEm bicycles factory can produce 100 bicycles in a day at a total cost of $10,100, and it can produce 120 bicycles in a day at a total cost of $10,700. A)Find a linear function that models the total cost for RideEm to produce x bicycles B) what are the companies daily ...

**Calculus**

A rectangle is to be inscribed under the curve y=4cos(.5x). The rectangle is to be inscribed from x=0 to x=pi. Find the dimensions that give max area and what is the max area.

**Calculus**

The length of the graph of f(x) = 2/3x^(3/2) over [0,p] equals 52/3. Find p. I think p is about 8.09.

**Calculus**

The length of a curve for 0 <= x <= 20 is given by the integral from 0 to 20 of √(1 + 84x^4) dx. If this curve contains the point (1,11), what is the equation of the curve? My answer is 3x^3 + 8.

**calculus**

If a ball is thrown into the air with a velocity of 48 ft/s, its height in feet t seconds later is given by y = 48t − 16t2. (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (i) 0.5 seconds ft/s (ii) 0.1 seconds ft/...

**Calculus**

If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) What is the average speed over the given time intervals? (i) [1, 2] (ii) [1, 1.5] (iii) [1, 1.1] (iv) [1...

**calculus**

If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) What is the average speed over the given time intervals? (i) [1, 2] (ii) [1, 1.5] (iii) [1, 1.1] (iv) [1...

**Calculus**

If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) What is the average speed over the given time intervals? (i) [1, 2] (ii) [1, 1.5] (iii) [1, 1.1] (iv) [1...

**Calculus**

If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by y = 52t − 1.86t2. (Round your answers to two decimal places.) (i) [1, 2] (ii) [1, 1.5] (iii) [1, 1.1] (iv) [1, 1.01] (v) [1, 1.001]

**Calculus**

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. x = 7y^2, y ≥ 0, x = 7; about y = 2

**Calculus help**

Find the area under the graph of f(x) = e-ln(x) on the interval [1, 2].

**Calculus 2**

Find the area bounded by the curves y=4x^2-25, y=0, x=-1, x=3.5. Ps the area is not 54 or 60 I already tried.

**Calculus help**

Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1180 ...

**Calculus 2**

Find the area of the region. Please show work so I can understand. 2y=5x^(1/2),y=3,2y+4x=9