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Section 2.6 Limits Involving Infinity; Asymptotes of Graphs
6. (a)
1 8
(b)
7. (a) 53 8. (a)
(b) 53
3 4
9. 1x
(b)
sin 2 x x
10. 31
cos 3
1 x
lim
x
sin 2 x x
31 lim
2t sin t t t cos t
11. lim
lim
t
r sin r r 2 r 7 5sin r
12. lim
14. (a)
2 x3 7 3 2 x x x x 7
0 by the Sandwich Theorem
cos 3
0 by the Sandwich Theorem
010 1 10
r
2 x 3 x 5 x 7
lim
lim 10 1 r 200 2
sin r r 7 2 r 5 sinr r
1
2 3x
lim
7 x 5 x
2 5
(b)
2 73 x 7 1 1 x 1 x 2 3
lim
lim
(b) 2 (same process as part (a))
16. (a)
17. (a)
x 1 2 x x 3
lim
3x 7 2 x x 2
lim
lim
lim
1 1 x x2
x 1
3
9 x4 x 4 2 x 2 x 5 x x 6
19. (a)
10 x5 x 4 31 x6 x
20.
x 3 7 x 2 2 2 x x x 1
(a) lim
2
0
(b) 0 (same process as part (a))
lim
x
lim
x
9
7 9
1
x3 2 52 13 64 x x x
10 1 31 x x 2 x6
1
0
lim
21. (a)
3 x 7 5 x 2 1 3 x 6 x 7 x 3
lim
9 2
(b)
9 2
(same process as part (a))
(b) 0 (same process as part (a))
, since x n 0 and x 7 .
x 7 2 x 1 1 2 x 1 x x
x 3 7 x 2 2 2 x x x 1
(b) 7 (same process as part (a))
x2
x 7 2 x 1 1 2 1 x x x
(b)
lim
x
x2
lim
lim
2
(b) 0 (same process as part (a))
7 3 x 1 x
lim
(same process as part (a))
0
lim
18. (a)
lim
3
x
2 5
x2
3 7 x x2
x 1
7 x3 2 x x 3 x 6 x
lim
3 4
2 1 sin t t t 1 cost t
lim
13. (a)
15. (a)
1 8
, since x n 0 and x 7 .
3 x 4 5 x 1 x 3 2 3 x 67 x 3 x
, since x n 0 and 3x 4 .
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Full file at https://testbankuniv.eu/Thomas-Calculus-Early-Transcendentals-14th-Edition-Hass-Solutions-Manual
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