24 STEP 2. Determine Your Test Readiness
- The velocity function of a moving particle
on thex-axis is given asv(t)=t^2 −t,t≥ 0.
For what values oftis the particle’s speed
decreasing? - The velocity function of a moving particle is
v(t)=
t^3
3
− 2 t^2 +5 for 0≤t≤ 6 .What is the
maximum acceleration of the particle on the
interval 0≤t≤6? - Write an equation of the normal line to the
graph off(x)=x^3 forx≥0 at the point
where f′(x)=12. - At what value(s) ofxdo the graphs of
f(x)=
lnx
x
andy=−x^2 have perpendicular
tangent lines?
- Given a differentiable functionfwith
f
(
π
2
)
=3 and f′
(
π
2
)
=−1. Using a
tangent line to the graph atx=
π
2
, find an
approximate value off
(
π
2
+
π
180
)
.
- An object moves in the plane on a path given
byx= 4 t^2 andy=
√
t. Find the acceleration
vector whent=4.
- Find the equation of the tangent line to the
curve defined byx= 2 t+3, y=t^2 + 2 t
att=1.
Chapter 10
- Evaluate
∫
1 −x^2
x^2
dx.
- If f(x) is an antiderivative of
ex
ex+ 1
and
f(0)=ln (2), findf(ln 2). - Find the volume of the solid generated by
revolving about thex-axis the region
bounded by the graph ofy=sin 2xfor
0 ≤x≤πand the liney=
1
2
.
- Evaluate
∫ 5
2
1
x^2 + 2 x− 3
dx.
- Evaluate
∫
x^2 cosxdx.
Chapter 11
- Evaluate
∫ 4
1
1
√
x
dx.
- If
∫k
− 1
(2x−3)dx=6, findk.
- Ifh(x)=
∫x
π/ 2
√
sintdt, findh′(π).
- If f′(x)=g(x) andgis a continuous function
for all real values ofx, then
∫ 2
0
g(3x)dxis
(A)
1
3
f(6)−
1
3
f(0)
(B) f(2)− f(0)
(C) f(6)− f(0)
(D)
1
3
f(0)−
1
3
f(6)
- Evaluate
∫x
π
sin (2t)dt.
- If a function f is continuous for all values of
x, which of the following statements is/are
always true?
I.
∫c
a
f(x)dx=
∫b
a
f(x)dx
+
∫c
b
f(x)dx
II.
∫b
a
f(x)dx=
∫c
a
f(x)dx
−
∫b
c
f(x)dx
III.
∫c
b
f(x)dx=
∫a
b
f(x)dx
−
∫a
c
f(x)dx
- Ifg(x)=
∫x
π/ 2
2 sintdton
[
π
2
,
5 π
2
]
, find
the value(s) ofx, whereghas a local
minimum.