Calculus III, mat 2213-5
Examination, March 10,1994
Instructor: D. Gokhman
Name:
1. (30 pts.) Determine whether the following series converge:
(a) โ
X
k=1
log(k)
โk(b) โ
X
k=1
(k!)3
(3k)! (c) โ
X
k=1 k
k+1
!k2
2. (20 pts.) Find the interval of convergence of
โ
X
k=1
(โ1)k
โk+2(3x+2)
k
3. (30 pts.) Find the second order Taylor approximation for
โlog (2 โx) at 1. Estimate the absolute error on [1/2,3/2].
4. (20 pts.) Find the first four nontrivial terms of the Maclaurin
series for the following functions:
(a) f(x)= x9
(2 โx)2(b) f(x)=x4(xโ1) ex3
Extra credit (5 pts.): What would they be for ex3+1?
1 2 3 4 5 total (100)
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