AP Calculus BC Practice Exam 2 423
- The correct answer is (B).
Since 0<ak≤bkfor allk,
∑∞
k= 0
ak≤
∑∞
k= 0
bk,
and since
∑∞
k= 0
bkconverges, by the comparison
test,
∑∞
k= 0
akconverges.
- The correct answer is (C).
Integrate
∫
xsec^2 xdxby parts. Letu=x,
du=dx,dv=sec^2 xdx, andv=tanx. Then
∫
xsec^2 xdx=xtanx −
∫
tanxdx
=xtanx+ln|cosx|+C.
Comparing to the given information,
∫
xsec^2 xdx= f(x)+ln|cosx|+Ctells us
thatf(x)=xtanx.
- The correct answer is (A) as shown below.
y
x
1
0
Place the solid on thexy-plane as illustrated in
the accompanying diagram.
Sincex^2 +y^2 =1,y=±
√
1 −x^2. Volume
V=
∫ 1
− 1
(
√
1 −x^2 −(
√
1 −x^2 ))
2
dx=
∫ 1
− 1
(2
√
1 −x^2 )
2
dx= 4
∫ 1
− 1
(1−x^2 )dx
= 4
([
x−
x^3
3
] 1
− 1
)
=
4
((
1 −
1
3
)
−
(
− 1 +
1
3
))
= 4
(
4
3
)
=
16
3
.
