1. Solve the initial-value problem.
2 , (0) 5
dx tx x x
dt
+ = =
. Use your solution to compute x(3).
a)
5e!6
b)
5e6
c)
6e5
d) 3 e) โ10
Ans: a
2. The volume of the solid generated by revolving the region bounded by the curves
x=y2
and y = x โ 2
about the y-axis
a)
20
!
3
b)
72
!
5
c)
42
!
5
d)
13
!
2
e)
32
!
5
f)
212
!
15
Ans b
3. Find the volume of the solid generated by rotating about the y-axis the region enclosed by y = sinx and
the x-axis from x = 0 to x = !.
4, Which of the following statements is true about the series
(!1)ncos 1
n
"
#
$%
&
'
n=0
(
)
? Be sure the work you
show justifies your choice.
a) the series is absolutely convergent
b) the series is conditionally convergent
c) the series is divergent
Ans: c
5. What is the interval of convergence of the series
n3x3n
n4+1
n=0
!
"
a) the series converges only at x = 0
b) the series converges for all x
c) the series diverges for x " 0
d) the series converges on (-1, 1]
e) the series converges on [-1, 1)
f) the series converges on [-1, 1]
