m232practicetest1key

m232practicetest1key - Math 232 Practice Test 1 Text...

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Math 232 Practice Test 1 Text Sections 4.4, 11.1–11.4 Answer Key 1 1. Determine whether the given sequence converges or diverges. If the sequence converges, determine the limit. (a) ! 2! ln 3 ( ) , 3! ln 4 ( ) , ! 4! ln 5 ( ) , 5! ln 6 ( ) , ...... diverges (b) cos n ! ( ) + sin n ! ( ) cos n ! ( ) " sin n ! ( ) # $ % & ' ( converges to 1 (c) n 2 + 10 n n 2 ! " # $ % & ' ( n ) * + , + - . + / + converges to e 10 ! (d) 9 n 6 + 3 n 4 ! 2 n + 100 5 n 3 + 8 n 2 + 4 " # $ % $ & ' $ ( $ converges to 3/5 (e) cos 5 ! n 2 + n + 6 20 n 2 + ! " # $ % & ' ( ) * + * , - * . * converges to 2 2 (f) ! e 2 , e 3 , ! e 4 , e 5 ,... converges to 0 2. Evaluate each limit without using a calculator . (a) lim x ! 1 ln x ( ) x 3 " 1 # $ % & ' ( = 1 3 (b) lim x !" 1 e cos x ( ) # $ % & ' ( does not exist (c) lim x !" ln ln x ( ) ( ) ln x ( ) # $ % & ' ( = 0 (d) lim x ! 1 x 1/ 1 " x ( ) ( ) = 1 e 3. Find the sum (if it exists) for the given infinite series. YOU MUST SHOW YOUR WORK! (a) ln 2 k + 1 k + 1 ! " # $ % & 1 ' ( diverges (b) 3 + 5 + 7 + 9 + 1 4 + 1 16 + 1 64 + 1 256 + !!! = 73 3 (c) 1 n 2 + 5 n + 6 ! " # $ % & 6 ' ( = 1 8 (d) 5 n 3 ! " # $ % & 1 ' ( diverges (e) 3 k 10 k + 1 1 ! " = 3 70 (f) 6 + 3 + 2 + 3 2 + 6 5 + 1 + 6 7 + 3 4 + 2 3 + 3 5 + 6 11 + !!! diverges 4. A ball is dropped straight down from an initial height of 30 feet. With each bounce straight upwards, the ball rises to 4/5 of its previous height. Find exact value for the total vertical distance traveled by the ball if it bounces forever.
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