Fall 2009 Math 151
3. Determine
 whether the funtion
2
Week in Review III
is
ourtesy: David J. Manuel
5.
Setion 2.3
lim x2 − 4x + 3.
of length 1 whih ontains a solution.
x→5
3. Compute
4. Compute
x2 + 6x + 5
.
x→−1 x2 − 3x − 4
√
x −3
lim
.
x→9 9 − x
lim
lim
2
x+h
h→0
−
h
2
x
3
2. Compute
.
lim r(t), where r(t)
2
t→1 4
t + 2t
t −1
i+
j
t+1
t−1
1
4
Compute lim x cos
x→0
x
3x + 2 ≤ f (x) ≤ x3 + 4
x ≥ −2, ompute lim f (x).
3. Compute
=
4. Find the horizontal asymptotes of
√
x2 + 2
.
3x − 6
when
Setion 2.5
and
tinuity...
Right
Limits
Maplets
and
loated
Conat
http://allab.math.tamu.edu/maple/maplets
(only works on OAL mahine, Callab mahine, or any mahine with Maple installed
on it)
2. Find the values for whih
x−2
.
x2 + 2x + 1
p
lim x2 + 7x − x .
lim
x→∞
x→1
1. Left
5x2 + 7
.
x→∞ 3x2 − x
lim
x→−∞
7. Given
2
Setion 2.6
1. Compute
5. Compute
6.
k that makes
if x ≤ 3
kx
f (x) =
2x + k if x > 3
ontinuous at x = 3 .
x−2
Compute lim cos
.
π
x→2
x2 − 4
6. Prove that there is at least one real solution
4
to the equation x + x = 5. Find an interval
1. Use the properties of limits to ompute
2. Compute
and why.
4. Find the
of
value
2
(overing 2.3, 2.5, 2.6)
1
 x −9
if x 6= 3
 1x − 3
if x = 3
ontinuous at x = 3 or not
f (x) =
f (x) =
x2
x2 − 9
− 5x + 6
is not ontinuous. Determine whih, if any, of
these disontinuities are removeable.
1
f (x) =