# C find the symmetric equations of the line of

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(c) Find the symmetric equations of the line of intersection of the planes P 1 and P 2 .

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CALCULUS II, FINAL EXAM 6 Problem 2 This problem has two separate questions. (Answer all the questions!) (a) Find the length of the arc of the circular helix with vector equation r ( t ) = h 3 cos( t ) , 3 sin( t ) , 4 t i when - 1 t 0. (b) Determine whether the (improper) integral Z 0 x 2 e - x dx is convergent or divergent. Evaluate the integral if it is convergent.
CALCULUS II, FINAL EXAM 7 Problem 3 Evaluate the following integrals (clearly show the techniques of integration you use): (a) Z 1 x p ln( x ) dx (b) Z x cos( x ) dx (c) Z - x 2 + x + 2 ( x - 1)( x 2 + 1) dx.

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CALCULUS II, FINAL EXAM 8 Problem 4 This problem has two separate questions. (Answer all the questions!) (a) Find the area of the region enclosed by the parabola x = y 2 - y and the parabola x = y - y 2 . (b) The region enclosed by the curve y = x and the line y = x and is rotated about the horizontal line y = - 1. Find the volume of the solid obtained in this way.
CALCULUS II, FINAL EXAM 9 Problem 5 This problem has two separate questions. (Answer all the questions!) (a) Find the radius and interval of convergence of the power series X n =1 ( - 1) n n 2 ( x + 5) n . Be sure to check any endpoints that exist!

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CALCULUS II, FINAL EXAM 10 (b) Use the Maclaurin series of the function cos( x ) = X n =0 ( - 1) n x 2 n
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