378 STEP 5. Build Your Test-Taking Confidence
- A functionfis continuous on [−1, 1] and
some of the values offare shown below:
x − 1 0 1
f(x) 2 b − 2
Iff(x)=0 has only one solution,r, and
r<0, then a possible value ofbis
(A) − 1 (B) 0 (C) 1 (D) 2
17.
∫− 2
− 3
5 x
(x+2)(x−3)
dx=
(A) limn→ 0
∫n
− 3
5 x
(x+2)(x−3)
dx
(B) n→lim− 3 +
∫− 2
n
5 x
(x+2)(x−3)
dx
(C) n→lim− 2 −
∫n
− 3
5 x
(x+2)(x−3)
dx
(D) nlim→− 3
∫n
− 3
5 x
(x+2)(x−3)
dx
18.
∫
dx
( 2 x− 1 )(x+ 5 )
=
(A) ln
∣∣
∣∣^2 x−^1
x+ 5
∣∣
∣∣+C
(B) ln
∣∣
2 x^2 + 9 x− 5
∣∣
+C
(C)
1
11
ln
∣∣
∣∣^2 x−^1
x+ 5
∣∣
∣∣+C
(D)
1
11
ln
∣∣
2 x^2 + 9 x− 5
∣∣
+C
- What is the average value of the function
y=2 sin(2x) on the interval
[
0,
π
6
]
?
(A) −
3
π
(B)
1
2
(C)
3
π
(D)
3
2 π
- If a particle moves in thexy-plane on a path
defined byx=sin^2 tandy=cos( 2 t)for
0 ≤t≤
π
2
, then the length of the arc the
particle traces out is
(A)
∫ π 2
0
√
sin^2 t+cos( 2 t)dt
(B)
∫ π 2
0
√
sin( 2 t)dt
(C)
√
5
∫ π 2
0
sin( 2 t)dt
(D) 2
∫ π 2
0
sin( 2 t)dt
- Given the equationy =3 sin^2
(
x
2
)
, what is
an equation of the tangent line to the graph at
x =π?
(A) y = 3
(B) y =π
(C) y =π+ 3
(D) y =x−π + 3
- Which of the following statements about the
series
∑∞
n= 1
(−1)n
n+ 3
is true?
(A) The series converges absolutely.
(B) The series converges conditionally.
(C) The series diverges.
(D) None of the above.
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