Thomas Calculus 13th [Solutions]

102 Chapter 2 Limits and Continuity
107. y
2/3
x 1
1/3
108. y sin
x
x
2 1
109. (a) y (see accompanying graph)
(b) y (see accompanying graph)
(c) cusps at x 1 (see accompanying graph)
110. (a) y 0 and a cusp at x 0 (see the
accompanying graph)
(b) y 3
(see accompanying graph)
2
(c) a vertical asymptote at x 1 and contains the
point 1,
3
(see accompanying graph)
3
2 4
CHAPTER 2
PRACTICE EXERCISES
1. At x 1: lim f ( x) lim f ( x) 1
x
1
1 x 1
lim f ( x) 1 f ( 1)
x
f is continuous at x 1.
At x 0 : lim f ( x) lim f ( x) 0
x 0 x 0
lim f ( x) 0.
x 0
But f (0) 1 lim f ( x)
x 0
f is discontinuous at x 0.
If we define f (0) 0, then the discontinuity at
x 0 is removable.
At x 1: lim f ( x) 1 and lim f ( x) 1
lim
x
x
1
1 x 1
f ( x) does not exist
f is discontinuous at x 1.
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