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Q: The region is formed by the graphs of y 4x and y 12-x. Find the volume of the solid obtained by revo...

A: For the shaded part the outer radius = 12-x and inner radius = 4sqrt(x).

Q: Calculate S3, S, and S5 and then find the sum for the telescoping series 410 n3n1 n +2 n-3 where Sk ...

A: to determine the first few partial sums and the sum to infinity of the given telescoping series

Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17...

A: Firstly, we calculate unit vector in direction of vector u.

Q: Determine if y=e−x+8x−9 is a solution to the initial value problem given by y′+1=8x−y and y(0)=−8.

A: The given differential equation is y′+1=8x−y.The solution of the deferential equation is given as, y...

Q: a. Determine whether the Mean Value Theorem applies to the function f(x)= ex on the given interval [...

A: Definition used: Mean Value Theorem

Q: Given f(x) = x^3 + 3x - 2 , find y = (f ^-1 (x))' at the point (2,1)

A: Click to see the answer

Q: how to find Find the exact length of the polar curve. r = θ2, 0 ≤ θ ≤ 7π/4

A: The polar curve I given as, r = θ2, 0 ≤ θ ≤ 7π/4.The formula to calculate the exact length of th...

Q: Find a particular solution to the differential equation below that passes through the point (−3,−5)....

A: The given differential equation is y’ = 5x–5.

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by x ...

A: We are given equations as

Q: This is solving the 2nd derivative of f(x) = x^2/ 1+e^x, and we have already obtained the 1st deriva...

A: The given function is,

Q: Find the area of the region that lies inside both curves. r = 9 + cos(θ), r = 9 − cos(θ)

A: To calculate the area of the given region (by integration) described by polar coordinates

Q: 3. Given the function g(x) 8x defined on [-1, 1], determine if the function satisfies the Mean Value...

A: Given,

Q: Differentiate the function. f(x) = (3x5 − 2)18

A: Consider the function:

Q: Find the volume of the solid generated when R (shaded region) is revolved about the given line. 28- ...

A: Consider a shaded disc as shown in the diagram on the white board.Radius, R = 14 - y; thickness = dx...

Q: Consider the differential equation dy/dt = y−y2. Given that y(0)=0.5, solve the differential equatio...

A: To find the expression for y(t) and find the limit y(t) as t tends to infinity

Q: Help w/ #6

A: The curve is given by ti+t2j+t3k.The formula to calculate the curvature of the curve is given by,

Q: How can I do this? Which is the result?

A: Given:The function is

Q: 3ln xy′−9x2 y′=4x4 What is the order of the differential equation shown above?

A: The given differential equation is ,3ln xy′−9x2 y′=4x4 The order of the differential equation is th...

Q: 2.5 Continuity 3. We would like to find a value of k to make the piecewise function f(x) continuous ...

A: 3)Answer: a) If I was to graph f(x) then the left part of 3 is changed when k is changed. As the k i...

Q: Need help with D, E, and F. Anser A- h= 17.92/(pi)r^2 Answer B-S(r)= 35.84/r + (pi)r^2 Answer C- S'...

A: Given information:The surafce area of the baking powder is shown below:

Q: Find the relative maxima, relative minima, and points of inflection, and sketch the graph of the fun...

A: Please see the white board for derivative of y, expressed as y'

Q: How can I get the result? Which is the result?

A: The function is given as

Q: Find the derivative of in two ways: first by applying the product rule and second by expanding the p...

A: Applied product rule and found f'(x).

Q: Find the derivative of y with respect to x

A: we are given an inverse function

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by abo...

A: Click to see the answer

Q: Find the point P on the line y = 5x that is closest to the point (52,0). What is the least distance...

A: Given:The equation of the line is y = 5x.(52,0) is the closest point to the point P which line on th...

Q: What two positive real numbers whose product is 56 have the smallest possible sum? Let S be the sum ...

A: Let x and y be the required positive real numbers.Given,

Q: The beginning of the question is attached. How do I argue that f(x) is concave if and only if g(x)=...

A: A function is concave or ceonvex is defined by the sign of its double derivative.A function is conve...

Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).

A: We first write the given function in the form of the definition of the derivative.

Q: find the exact length of the curve of the equation in the picture below make sure to show all work

A: The given curve equation is,

Q: Let H(x)=4f(x) + 5g(x), where the graphs of f and g are shown in the figure. Find H`(1).

A: Firstly, we find the function y=f(x) , which is linear function , as it is a equation of straight ...

Q: If f(x) 3x-2then f(x) = x 2x+ 2x5/3 2x 2x-1 12 1+5x8/3 3x2 2x-53-3x-3/2 x2 none of the above

A: The given function is,

Q: You must get from a point P on the straight shore of a lake to a stranded swimmer who is 60 meters f...

A: Let, "u" be the velocity at which you can swim and "v" be the velocity at which you can run.u = 2 m ...

Q: Determine whether the following series converges. Justify your answer 9(4k)! Σ k=1 (kl)* Select the ...

A: Consider the given series:

Q: How can I get the result? Which is the result?

A: The definite integral is given as

Q: Please help

A: Here we will make the use of series for sin(x2) to solve the given integral.The provided integral is...

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: Given infromation:The given funcion is

Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that...

A: To find the number of units completed in t hours by the new employee, integrate the rate of performa...

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R i...

A: The given curves are y=x, y=4x, y=16.The graph of the region formed by these curves is,

Q: Please show as much steps as possible as I am doing my best to fully understand how to solve these t...

A: Given function is,

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: The given interval is [-1,1] and the function is,

Q: How can I get the result? Which is the result?

A: we are given a graph and locate direction

Q: One of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate with ...

A: (a) can be integrated using power rule. (b) can not be integrated using power rule because (b) has t...

Q: How can I get the result? Which is the result?

A: Click to see the answer

Q: Which is the result?

A: We are given a function as

Q: For the sequence 1, 4, 7, 10,..., its nth term is Preview My Answers Submit Answers ou have attempte...

A: The given sequence is 1,4,7,10, ...

Q: Hello, I need help understanding how to form a general formula, using f(x)=5 tan x, for all the sol...

A: Consider the provided function.

Q: a), b) and c) please. I also forgot how to write interval notation....

A: To find the direction we have to graph the function v(t)= 3t^2-36t+105 ; [0,8]. And then we check th...

Q: dy If y 22 x, then dx 9.7 1. O 22 0. O 5. N O O O OO

A: The given equation is y=22+x.

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.