Answer calculus ii final exam 3 question 6 determine

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Answer: . . . . . . . . . . . . . . . . . .
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CALCULUS II, FINAL EXAM 3 Question 6 Determine whether the improper integral is convergent or divergent. Evaluate the integral if it is convergent. Z 1 1 x 1 . 1 dx Answer: . . . . . . . . . . . . . . . . . . Question 7 Find the area of the region bounded by the curve y = x 2 and the line y = x . Answer: . . . . . . . . . . . . . . . . . . Question 8 Evaluate the indefinite integral Z sin 7 ( x ) cos( x ) dx . Answer: . . . . . . . . . . . . . . . . . .
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CALCULUS II, FINAL EXAM 4 Question 9 Evaluate the indefinite integral Z x 2 1 + x 2 dx . Answer: . . . . . . . . . . . . . . . . . . Question 10 Determine whether the alternating series X n =1 ( - 1) n n 2 + 6 n 4 + 2 is divergent, absolutely conver- gent, or conditionally convergent. Answer: . . . . . . . . . . . . . . . . . .
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CALCULUS II, FINAL EXAM 5 PART II Each problem is worth 12 points. Part II consists of 5 problems. You must show your work on this part of the exam to get full credit. Displaying only the final answer (even if correct) without the relevant steps will not get full credit - no credit for unsubstantiated answers . CIRCLE YOUR ANSWER! Problem 1 Two planes are given by the equations x + y + z = 1 for the plane P 1 and x - 2 y + 3 z = 1 for the plane P 2 . (a) Find the coordinates of a point of intersection of the planes P 1 and P 2 . (b) Find the normal vector (i.e., the vector perpendicular) to the plane P 1 and the normal vector to the plane P 2 .
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