Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the y-axis.  y = x, y = 7x, y = 21

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A: we have x3+ex =0to check number of roots we can draw graph of both and check number of intersection

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A: You must have idea about Calculus in order to get the answer for these questions.

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A: To solve the following problem

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A: Solution of given question is written in below steps.

Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

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A: Find an equation of the tangent line to the curve y= 3cos-1(x/2) at the point (1,4π) .

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A: We can find the required time as below.

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A: Let's integrate given integral.

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Q: Find the following for the given equation. r(t) = e−t, 8t2, 3 tan(t)   (c)  Find r'(t) · r''(t).

A: Find the following for the given equation. r(t) =< e−t, 8t2, 3 tan(t) >   (c)  Find r'(t) ·…

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A: Avg value is given by below

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Q: Define a polynomial function with all of the following properties. Roots: x=7, x=-8, x=0. It bounces…

A: Given problem:- Define a polynomial function with all of the following properties. Roots: x=7, x=-8,…

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