### Implicit Differentiation Functions

Find y" for x^2/a^2 - y^2/b^2 = 1

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Find y" for x^2/a^2 - y^2/b^2 = 1

I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also c

I am trying to figure out a powers series representation for the function f(x) = e^x, centered at c = -2. I also need to find the interval of convergence.

Find an equation of the tangent line to the curve Y= x3 - 3x2 + 5x that has the least slope.

Find an equation of the tangent line to the curve, Y = x^3 - 3x^2 + 5x that has the least slope. Make sure to show all of the required steps.

A billiard ball is hit and travels in a line. If s centimeters is the distance of the ball from its initial position at t seconds, then s=100t2 + 100t. If the ball hits a cushion that is 39cm from its initial position, at what velocity does it hit the cushion?

Create a proof to show that the following is true. a x (b+c) = a x b + a x c

A special window has the shape of a rectangle surrmounted by an equilateral triangle. If the perimeter is 16 feet, what dimensions will admit the most light? (hint: Area of equilateral triangle = the square root of 3/4 times x squared.)

I am stuck on how to solve the sum of the series that I have attached in a word document.

I used the product to sum identities rule since the integral involved cosines of different angles. I have attached a word document with the integral to solve and my work. I want to know if my answer is correct. If my answer is not correct, I want to know the correct answer and the steps to get it. Thanks.

Write an equation and sketch a graph of the line through the points (-4,-3) and 3,12)

We are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula and the answers I received in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained

NOTE: we are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained.

I need to see how to find the centroid coordinates by using integrals and moments. I have attached a word document with the formulas we are supposed to use to find the centroid. Now here is the problem: Given: y = 9 - x^2, y = 2 Find the coordinates of the centroid of the above plane region. Please refer to the atta

Given: y = -x^2 + 4x defined on the closed domain [0,4] a) sketch the graph b) Revolve the graph about the x-axis. Find the area of the surface obtained.

Given: f(x)=2x, g(x)=10 a)Sketch the plane region bounded by the functions graphs and the y-axis b)Use the shell method to find the volume of the solid formed by revolving the above plane region about the y-axis. NOTE: the graph I did is attached. The answer I got was 523.599. I'm trying to check to see if I did the gr

Given: f(x)=2x, g(x)=x, x=5 a)Sketch the plane region bounded by the functions graphs b)Use the washer method to find the volume of the solid formed by revolving the above plane region about the x-axis.

Solve each of the following differential equations: ***For each problem,state the method you used and show the work required to obtain the answer.*** 1) (y-(cos^2)x)dx + cosxdy=0 2) ye^x dx= (4+e^2x)dy

The function f(x)=2x^3 - 33x^2 + 108x - 6 has two critical numbers. The smaller one equals ______ and the larger one equals______.

The steps for integrating sine to an odd power of 3 or higher are shown using the example Ssin^5(x)dx. The solution is detailed and well presented.

Given the differential equation: (y^4)(e^2x) + y' = 0 NOTE: The differential equation above is attached in a microsoft word document for better legibility. Additionally my work is attached as a jpeg file. The questions: a)Find the general solution. b)Find the particular solution such that y(0) = 1.

At 10:00 AM, an object is removed from a furnace and placed in an environment with a constant temperature of 68 degrees. Its core temperature is 1600 degrees. At 11:00 AM, its core temperature is 1090 degrees. Find its core temperature at 5:00 PM on the same day.

A Farmer wants to construct a fence. The area that he is going to enclose is rectangular, but one of the sides is a river (assumed to be straight). If he has 120 m of fence, what is the maximum surface that he can enclose?

Explain why the graph of f(x) is rising over an interval a < or equal to x < or equal to b if f '(x) > 0 throughout the interval. What can you say about the graph of f if f '(x) is less than zero on a < or equal to x < or equal to b?

The formal definition of the limit is explained using the example lim x->5 2x = 10.

1. The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 320 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decreas

I need an overview of geometric applications for calculus.

Given the points (3,7) and (-1, 3), find the slope of the line containing these 2 points, find the distance between these 2 points and find the midpoint.

1. A weather balloon is rising vertically at a constant rate of 4 ft/s directly above a straight and level road. When the balloon is 75 ft above the road, a car moving at 55 ft/s passes directly under the balloon. Based on this information find: a. the rate the distance between the balloon and the car is changing 3 sec after t

The procedure is shown using the easy example y=(5x^4+3x^2-2)^7.