CALCULUS III Math 2214 Nunley CALCULUS II EXAM 4 · Show all work. Answers without work or explanation will not be given full credit. 1) Find the limits of the following sequences: a) 3 2 n n n) (1 lim...

Calculus


CALCULUS III Math 2214 Nunley CALCULUS II EXAM 4 · Show all work. Answers without work or explanation will not be given full credit. 1) Find the limits of the following sequences: a) 3 2 n n n) (1 lim + ¥ ® b) 2 n 3 lim 2 n n + ¥ ® c) n n lim a ¥ ® where 1 ; 2 1 1 = - = + a a a n n 2) Determine whether each of the following series converge or diverge. Give a full explanation as to why you made your decision. a) å ¥ = 1 n n n! 5 b) å + ¥ = 1 n 2 2 n 3 6 c) å ¥ = 1 n n n 3 n d) å ¥ = 1 n n ln(n) 3) Find the sum of the series å ¥ = 1 n 2n n 5 2 - 4) a) Find the Taylor polynomial of degree 3 based at 4 for x . b) Use your answer in a) to estimate 2 . How close is your estimate to the true value? c) Would you expect your polynomial to give you a better estimate for 2 or for 3 ? Why? 5) Let f(x) = å ¥ = + 0 n n n n 5 3) (x (-1) . Find the interval of convergence for f(x). 6) A ball is dropped from a height of 20 feet. Each time the ball hits the ground, it rebounds to 40% of its previous height. Find the total distance that the ball travels. _1191216419.unknown _1246342018.unknown _1436344248.unknown _1436344549.unknown _1467023331.unknown _1436344280.unknown _1246342044.unknown _1246342073.unknown _1246341890.unknown _1246341950.unknown _1191216433.unknown _1191216325.unknown _1191216392.unknown _1191216259.unknown