Calculus

1 (TCO 2 ) Find the nth term for the geometric sequence with the given values : 2 /3 , 2 , 6 n 6 (Points : 2

162

231

180

153

2 (TCO 2 ) Find the nth term for the geometric sequence with the given values : a1 24 , r , n 10 (Points : 2

1 /8

3 /16

2 /9

3 /64

3 (TCO 2 ) Find the value a1 for the geometric sequence with the given values : r 5 /2 , n 4 , S4 812 (Points : 2

16

32

24

p 64 (Points : 2

1 /3

1 /5 (Points : 2

Converges 5 /2

Converges 3 /2

Converges 7 /2

Diverges

6 (TCO 2 ) The value V (in dollars ) of a certain investment after n years can be expressed as V 100 (1 .06 1 .062 1 .063 1 .06n . By finding partial sums , determine whether this series converges or diverges (Points : 3

converges diverges

7 (TCO 2 ) Find the first three nonzero terms of the Maclaurin expansion of the function . f (x 9 sin x (Points : 3 (Points : 3

9 (TCO 2 ) The displacement y (in cm ) of an object hung vertically from a spring and allowed to oscillate is given by the equation shown below where t is the time (in s . Find the first three terms of the Maclaurin expansion of this function . y 9e-0 .5t cos t (Points : 3

9 , -4 .5t , -3 .375t2

9 , 4 .5t , -3 .375t2

9 , 4 .5t , 3 .375t2

-9 , -4 .5t , -3 .375t2 (Points : 3

0 .0713

0...