# Math 112 Solutions for 2.2, p.100

1.
(a) about 1.2. (b) about -1. (c) 0 (d) 0 (e) 0 (f) about . (g) 1 (h) DNE

2.
(a) The limit is 5 because the line passes through the point (4, 5). (b) 6. (c) 1. (d) -1. (f) -5. (g) 1. (h) DNE. (j) DNE. (l) 0. (n) 0. (p) DNE.

3.
(a) .

(b) The graph of is between .499 and .501 for .

(c) . If , then and . If , then , so let , or .

(d) . If , then and . If also , then , so let . Then .

4.
(b) Since , plot in the window . The graph appears between and . Hence we may choose .

5.
(a) Let . Then .

(c) . If , then . Let . Then .

6.
(a) Given , let . Then .

(b) Let be given, and let . Then .

(c) . If , then . Hence, given , let . Then .

(d) . Let . Then , so and . Now given , let . Then .

11.
Suppose both and as , with . Let . Then there exists such that and there exists such that . Hence, if , then , a contradiction.

14.
(a) . (b) . (c) . (d) -1. (e) 1. (f) DNE. (g) DNE. (h) DNE. (i) DNE. (j) 0. (k) 0. (l) 0.

16.
(b), (c), and (d) are true.

17.
For example, if , then . ; .