MA 3972-MA-Book April 11, 2018 16:20
380 STEP 5. Build Your Test-Taking Confidence
- The graph offconsists of two line segments
and a semicircle for− 2 ≤x≤2 as shown
below. What is the value of
∫ 2
− 2
f(x)dx?
y
x
f
1
0
(A) − 2 − 2 π (B) − 2 −π
(C) − 1 −
π
2
(D) 1+
π
2
- What is the average value of the function
y=3 cos(2x) on the interval
[
−
π
2
,
π
2
]
?
(A) − 2 (B) −
2
π
(C) 0 (D)
1
π
- Iff(x)=|x^3 |, what is the value of limx→− 1 f′(x)?
(A) − 3 (B) 0
(C) 1 (D) 3
- A spherical balloon is being inflated. At the
instant when the rate of increase of the volume
of the sphere is four times the rate of increase
of the radius, the radius of the sphere is
(A)
1
4
√
π
(B)
1
√
π
(C)
1
π
(D)
1
16 π
- If
dy
dx
=
x^2
y
and atx=0,y=4, a solution to
the differential equation is
(A) y=
x^3
3
(B) y=
x^3
3
+ 4
(C)
y^2
2
=
x^3
3
(D)
y^2
2
=
x^3
3
+ 8
- The area of the region enclosed by the graph of
x=y^2 −1 and they-axis is
(A) −
4
3
(B) 0
(C)
2
3
(D)
4
3
- The graph off′, the derivative off, is shown
below. At which value ofxdoes the graphf
have a horizontal tangent?
x 1 0 x 2 x 3
y
x
f′
(A) x 1 (B) 0
(C) x 2 (D)x 3
- If f(x)=−|x− 3 |, which of the following
statements aboutf is true?
I. fis differentiable atx=3.
II. fhas an absolute minimum atx=3.
III. fhas a point of inflection atx=3.
(A) II only
(B) III only
(C) II and III only
(D) None
STOP. AP Calculus AB Practice Exam 2 Section I Part A
