# Find the taylor series about a 0 for 1 1 2 x 2 ans b

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6. Find the Taylor series about a = 0 for 1 1 + 2 x 2 . Ans: b 7. What is the length of the part of the curve y = x 2 ! ln x 8 between the points (1,1) and ( e 2 , e 2 1 8 ) ? Ans d 8. Integrate: 3 x + 2 x 2 ! 4 dx 0 1 " a) -2 b) -3ln2 + ln3 c) ln2 d) ! /4 e) 0 f) ln(3) Ans: b

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9 Is the area S finite or infinite? If finite, what is the area? 10. Evaluate the following integral: dx x x ! 1 0 4 ln 3 Ans a 11. Evaluate the integral or show it is divergent : dx x ln x 1 ! "
12. The base of a solid is the region enclosed by the ellipse 4 x 2 + y 2 = 1 . If all the plane crossections perpendicular to the x axis are semicircles, compute the volume of the solid. a) ! 6 b) ! 4 c) ! 3 d) ! 2 e) 2 ! 3 f) 3 ! 4 Ans c 13. Which of the following statements about the alternating series ( ! 1) n a n n = 1 " # where a n = n 1 + n 2 is true?

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