Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis. 1 y = - y = 0, x1 = 1, x2 = 4 V = Sketch the region and a typical shell. (Do this on paper. Your instructor may ask you to turn in this sketch.)

Q: Test the series below for convergence using the Root Test. 2n + 6 4n + 2 n=1 The limit of the root…

A: Root Test : Consider the positive term series ∑ an . Define ,             L = limn→∞ an1n  , then(i)…

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A: Given:     radius ( r ) = 4 cm

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A: Let's find.

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A: We can find the derivative as below.

Q: Consider the following. (If an answer does not exist, enter DNE.) F(x) = x/6 – x (a) Find the…

A: I am attaching image so that you understand each and every step.

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A: Note: As there are three different questions, according to policy of our company we will solve the…

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A: Solved below

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Q: 3. Find an equation of the hyperbola having foci at (4, 3-V 52) and (4, 3 +/52) and asymptotes at y=…

A: Focii: (4, 3+52) &amp; (4, 3-52)Assymptotes : y=3x2-3 , y=-3x2+9Let vertex by represented by (h,k)…

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A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: Use the General Power Rule to find the derivative of the function. g(x) =    9 − 7x g'(x) =

A: We have to find g'(x) using the general power rule.

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Q: Which one is the sum of the geometric series 1 00 n= O 2 O 3 | 2 O Divergent 3/4

A: The sum of an infinite geometric series is given by, Sn=∑n=0∞arn=a1-r if r&lt;1 a is the first term…

Q: 3) Find the average value of the function f (x) = 2sin ( Tr) cos ( Tx) on the interval [1,5]. --;…

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Q: Find a positive number z such that the sum of its reciprocal and 5,324 times its square is as small…

A: This question is related to algebraic equations, we will solve it using given information.

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A: Solving the problem by finding the value of definite integral.   NOTE :: As per our Expert…

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Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

A: By using Newton's backward difference formula to find the approximate value of y-13 when…

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Q: Given the differential equation y" = 4y' - 3sin(4y) Find the Implicit derivative " dy/dx" of the…

A: Given problem:- Given the differential equation   y" = 4y - 3sin(4y)   Find the Implicit derivative…

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Q: Find the derivative of the logarithmic function. y = In 6 + e 6- e*. Step 1 The given function y =…

A: We will derivate the function step wise as asked in the question.