1
151 WebCalc Fall 2002-copyright Joe Kahlig
Quiz #3
MATH 151 Section
Name:
September 12, 2002
1. Compute these limits. Give exact answers.
x2 − x − 30
(x − 6)(x + 5)
x+5
11
= lim
= lim
=
x→6 x2 − 9x + 18
x→6 (x − 6)(x − 3)
x→6 x − 3
3
7
(b) lim+
= −∞
x→7 7 − x
(a) lim
The way to approach this problem is to realize that if you plug in a 7 for x you get 7/0.
This means that there is a vertical asymptote at x = 7. Now look at the graph and you
will see that as you go to 7 from the positive direction the function goes to −∞.
The other way to work this problem is to put in numbers getting closer to 7 and seeing
what the results go toward.
x
7.5 7.1 7.01 7.001
f (x) -14 -70 -700 -7000
1
2+h
− 12
(c) lim
= lim
h→0
h→0
h
−1
−1
lim
=
h→0 2(2 + h)
4
2
2(2+h)
−
(2+h)
2(2+h)
h
= lim
2−(2+h)
2(2+h)
h→0
h
=
−h
2(2+h)
lim h
h→0
1
2. If f (x) is the piece-wise defined function, compute these limits.
(
f (x) =
lim f (x) = lim
x→2+
x→2+
2x
4
=
x+5
7
3x2 + 1
2x
x+5
for x < 2
for x ≥ 2
= lim
h→0
−h
1
∗ =
2(2 + h) h