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 atangent line to the graph atx=
π
2, find anapproximate 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
∫ 521
x^2 + 2 x− 3dx.- Evaluate
∫
x^2 cosxdx.Chapter 11- Evaluate
∫ 411
√
x
dx.- If
∫k− 1(2x−3)dx=6, findk.- Ifh(x)=
∫xπ/ 2√
sintdt, findh′(π).- If f′(x)=g(x) andgis a continuous function
for all real values ofx, then
∫ 20g(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
∫xπsin (2t)dt.- If a function f is continuous for all values of
x, which of the following statements is/are
always true?
I.∫caf(x)dx=∫baf(x)dx+
∫cbf(x)dxII.
∫baf(x)dx=∫caf(x)dx−
∫bcf(x)dxIII.
∫cbf(x)dx=∫abf(x)dx−
∫acf(x)dx- Ifg(x)=
∫xπ/ 22 sintdton[
π
2,
5 π
2]
, find
the value(s) ofx, whereghas a local
minimum.