
15
if x < −7



8 − x if − 7 ≤ x < 4
Example 6.7 Let f (x) =
.

−1
if x = 4



8
if x > 4
Sketch a graph of f (x).
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
−1
−2
−12−11−10−9−8−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7 8
Evaluate the limits:
(a)
(b)
x→−1
lim f (x) = 15
x→−7+
(c) lim f (x) = 15
x→−7
(d) lim− f (x) = 4
x→4
(e) lim f (x) = 8
x→4+
(f) lim f (x) does not exist
x→4
Example 6.8 Evaluate the limits, if they exist:
(a) lim
lim f (x) = 15
x→−7−
x+1
1
=−
2
x −1
2
x2 − 5x + 6
does not exist
x→5
x−5
(b) lim
(x + h)3 − x3
= 3x2
h→0
h
1
1
(d) lim
−
= −∞
x |x|
x→0−
1
1
(e) lim
−
=0
x |x|
x→0+
(c) lim
1