Math 142 (Section 501) Test 3 April 22, 2008
Name
1. (10 points) Complete the list below by writing down the Maclaurin series and the interval of
convergence for each function.
=1+m+32+$3+m4+$5+~- fo
Math 142 (Section 501) Integration Practice II (Solutions) Spring 2008
1. Evaluate the following integrals
X51713" f7; are/WA)!
(a) f sesin 3x dx 727-
I
"/"
?
r r
.5 gX?/}X "1"?219ng _[ C
Var
(c)
Math 142 (Section 501) Test 1 Spring 2008
Name M-
1. (7 points eah) Evaluatethe following integrals. Simplify your answer in parts (a)~(d).
ll'l (h) ftanxsec3scdx walk 5 /L
Lid %
[714/5 {Gib/FM}; I
Math 142 (Section 501) Integration Practice I (Solutions) Spring 2008
1. Evaluate the following indenite integrals.
(a) /(10224 + g - 38mm ~15) dx
:3 2x54. 9 IMXvJrayrx xiéijc (d) fcos3(x)sin(x)dx :fé
Math 142 (Section 501) Quiz 10 April 1, 2008
Name .ZQL' 0 5'
1. Determine if the following series converge or diverge. You must fully justify your answers.
°°k2+15 3? K7 2"
. r
a '_.!.,. If
WK K?
Math 142 (Section 502) Quiz 7 March 4, 2008
Name
1. (3 points) The region between the maxis and the curve 3: = 6 on the interval [0, 00) is
revolved around the maxis. Compute the resulting volume.
v
Math 142 (Section 501)
Quiz 12 Solutions
Spring 2008
1. The following innite series converges to a sum S. S= 1 1 1 1 1 1 (1)k+1 = 1 + + + 2 3 4 5 6 k k=1
(a) There are two conditions that are necessar
Math 142 (Section 501)
Let R denote the region between the graph of y = 553/2 and y z 8 on the interval [0, 4]. Using
two ways for each problem, set up and evaluate denite integrals which represent
Math 142 (Section 501) . Quiz 5 February 25, 2008
Name
1. (4 points) Evaluate the following integral.
dac
. f(1+4m2)2
I ix 9' 7.: d3 (Let2x:tawa
:[m
(1+Zav')? ,
5/ y¢feoa§/ 1+4 9.x
I 2. (3 poin
Math 142 (Section 502) Quiz 8 March 17 , 2008
Name
1. (2 points) Write out the rst ve terms of the sequence, determine if the sequence converges,
and if so nd its limit.
{ 5n + 1 F
10; + 1 n=1
.7 -
Math 142 (Section 501)
Quiz 9 Solutions
Spring 2008
1. Determine if the following series converge or diverge. If a series converges, then you should also compute its sum.
(a)
k=0
e1-2k = e +
1 1 1 1 +
Math 142 (Section 501)
Quiz 11 Solutions
Spring 2008
Determine if the following series converge or diverge. You must fully justify your answer. 1. 5k k=3 k!
Since this series has positive terms, we ma
Math 142 (Section 501) Quiz 2 Solutions Spring 2008
1. The graphs of f (:12) = 3:2 - 21 and g(x) = 43': are sketched below and the area. between the
two curves is shaded in. Determine the exact area o
Math 142 (Section 501) Quiz 4 Solutions Spring 2008
1. Set up, but do not evaluate, integrals which represent the following quantities.
(3) Length of the curve y 2 team for a: on the interval [7r/3,0]
Math 142 (Section 501) Quiz 3 Solutions Spring 2008
Let R denote the region between the graph of y = 3:3 + :1: and the xaxis on the interval [0, 1]. Set
up, but do not evaluate, denite integrals which