Math 31
1.
Review: Rates of Change: Motion Name _
& Related Rates
32
3
A particle travels along a path defined by s = t t 6t + 12, t >0
2
a.
what is the average velocity during the first 5 seconds?
b.
what is the velocity at t = 3 ?
c.
what is the average
Integration & Area Review
Math 31
Name
_
A.
Integrate the following:
1.
F
z5x
H
3.
d
z
5.
z
7.
zc
page 2
2
3
1
i
3 sec2 x x dx
2e 7 x dx
h
7
2 x 2 2 x 3 8 dx
Math 31
WmarEros/06/03
3
5
F
G
z
H
4.
zb
z
8.
Idx
K
2.
6.
7x 4 + 2x
z
Integration & Area Review
Math 31 Graph Sketching Review
1.
Find the following limits:
a.
c.
2.
Name _
lim
x +
lim
x 1
4 x2 + x
x
x 1
x2 x + 1 x
b.
3 x 4 + 5 x 2 2
lim
x x 2 2 x3 + 5 x 4
d.
2 x
lim x +
x 3+
x 3
Find the equation(s) of the asymptote(s) of each of the
following
Extreme Values Review
Math 31
1.
a.
Name_
Given the following functions, find:
the critical numbers
b. the intervals of increase and decrease
c. the coordinates of the points where the maximum
or minimum occur. Determine if the points are
maximum or minim
Math 31/IB
Chapter 2: Derivative Review
Name_
dy
for
dx
2
3
4
y = x 6 + 11 2
3
x
x
b.
c.
y = 3 54 x 2
d.
e.
x2 2x
f ( x) =
x
3
f. y = x
g.
1.
Find
a.
1.
y=2 x
i.
y=
RossShepMath 10/2009
4
each of the following:
1
2x
( 4 x)
3
=
f ( x) =
2 ( x + 3)
2
2
x
y
Chapter 8: Exponential and Logarithmic Functions
Review
Name _
Math 31
1.
Find
dy
if:
dx
a.
( x 7)
y = ln
c.
6
b.
y = ln[5 ( x 8 ) ]
y = ln ( tan 2 x )
d.
y = ln ( 5 x 2 + x )
e.
log 3 ( 4 x 2 )
f.
y = log ( sec x )
g.
x2 3
log 4
5x + 7
h.
y = 3x 2 l