MA 3972-MA-Book April 11, 2018 16:20
378 STEP 5. Build Your Test-Taking Confidence
- What is the limh→ 0
csc(π/ 4 +h)−csc(π/ 4 )
h
?
(A)
√
2 (B) −
√
2
(C) 0 (D) −
√
2
2
- Iff(x) is an antiderivative ofx^2
√
x^3 + 1
and f(2)=0, thenf(0)=
(A) − 6 (B) 6
(C)
2
9
(D)
− 52
9
- If a functionfis continuous for all values ofx,
which of the following statements is/are always
true?
I. 2
∫b
a
f(x)dx=
∫ 2 b
2 a
f(x)dx
II.
∫b
a
f(x)dx=
∫a
b
−f(x)dx
III.
∣∣
∣∣
∫b
a
f(x)dx
∣∣
∣∣=
∫b
a
|f(x)|dx
(A) I only
(B) I and II only
(C) II only
(D) II and III only
- The graph offis shown below, andf is twice
differentiable. Which of the following has the
largest value:f(0), f′(0), f′′(0)?
(A) f(0)
(B) f′(0)
(C) f′′(0)
(D) f(0) andf′(0)
f
x
y
0
11.
∫
x^4 − 1
x^2
dx=
(A)
x^3
3
+x +C
(B)
x^3
3
−x +C
(C)
x^3
3
−
1
x
+C
(D)
x^3
3
+
1
x
+C
- Ifp′(x)=q(x) andqis a continuous function
for all values ofx, then
∫ 0
− 1
q(4x)dxis
(A) p(0)−p(−4)
(B) 4p(0)− 4 p(−4)
(C)
1
4
p(0)−
1
4
p(−4)
(D)
1
4
p(0)+
1
4
p(−4)
- Water is leaking from a tank at a rate
represented by f(t) whose graph is shown
below. Which of the following is the best
approximation of the total amount of water
leaked from the tank for 1≤t≤3?
(A)
9
2
gallons
(B) 5 gallons
(C) 175 gallons
(D) 350 gallons
123
50
100
150
200
f(t)
gallons/hour
t
(hours)
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