# Math 112 Solutions for 2.6, p. 167

1.
(a) about -1.97. (b) . (c) , so . (d) .

2.
(c) Assume that the function has value 0 at . The graph never straightens out, indicating nondifferentiability at the origin.

(d) Assume the function has value 0 at . The graph eventually flattens out, indicating that the derivative at 0 is 0.

3.
(c) . (e) .
4.
(b) . (c) .
5.
(a) (i) The one-sided limits of at 1 are both 1, so is continuous at 1. (ii) . The two one-sided limits of this expression are both 2, so .

(b) (i) The one-sided limits are not equal, so the function is not continuous at 1. Since it is not continuous at 1, it is not differentiable at 1.

(c) (i) The one-sided limits at -1 both have value 5, so is continuous at 5. (ii) . The two one-sided limits of this expression are both -2, so is differentiable at -1 and the derivative is -2.

6.
Assume that and all have value 0 at 0.

(a) does not exist, so is not continuous at 0.

(b) , so is continuous at 0. But , which does not exist, so is not differentiable at 0.

(c) , so is continuous at 0. , so is differentiable at 0.

11.
14.
and .

17.
Derivative is slope, so the derivative of a linear function is the (constant) slope of its graph.

20.
(a) .33 (c) .12, .23, and .175