Thomas Calculus 13th [Solutions]

82 Chapter 2 Limits and Continuity
8. (a) (b)
(c)
lim f ( x) 0 lim f ( x)
x
1 x 1
Yes, lim f ( x ) 0 since the right-hand and left-hand
x
1
limits exist and equal 0
9. (a) domain: 0 x 2
range: 0 y 1 and y 2
(b) lim f ( x)
exists for c belonging to (0, 1) (1, 2)
x c
(c) x 2
(d) x 0
10. (a) domain: x
range: 1 y 1
(b) lim f ( x)
exists for c belonging to
x
c
( , 1) ( 1, 1) (1, )
(c) none
(d) none
11. lim x 2 0.5 2 3/2
x 1 0.5 1 1/2
3
x 0.5
12. lim x 1 1 1
x 2 1 2
0 0
x 1
2( 2) 5
13. lim x 2x
5 2 (2) 1 1
x 1 2 2 1 2
( 2) ( 2) 2
x 2 x x
14. lim 1 x 6 3 x 1 1 6 3 1 1 7 2
x 1 x 7 1 1 1 7 2 1 7
1
x 1
15.
2 2 2
h 4h 5 5 h 4h 5 5 h 4h
5 5
lim
lim
h
h
2
h 0 h 0
h 4h
5 5
h( h 4)
lim
0 4 2
2
h 0 h h 4h
5 5 5 5 5
2
( h 4h
5) 5
lim
2
h 0 h h 4h
5 5
16.
2 2 2
6 5h 11h 6 6 5h 11h 6 6 5h 11h
6
lim
lim
h
h
2
h 0 h 0
6 5h
11h
6
2
6 (5h 11h 6) h(5h
11) (0 11)
lim
lim
11
2 2
h 0 h 6 5h 11h 6 h 0 h 6 5h 11h
6 6 6 2 6
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