   Chapter 2.3, Problem 47E

Chapter
Section
Textbook Problem

The signum (or sign)function, denoted by sgn, is defined by sgn x = { − 1   if   x <0   0   if   x = 0   1   if   x > 0 (a) Sketch the graph of this function.(b) Find each of the following limits or explain why it does not exist.(i) lim x → 0 + sgn x (ii) lim x → 0 − sgn x (iii) lim x → 0 sgn x (iv) lim x → 0 | sgn x |

(a)

To determine

To sketch: The graph of the signum function, sgnx={1if x<00if x=01if x>0.

Explanation

Use the function sgnx=1 when x<0, sgnx=0 when x=0 and sgnx=1 when x>0

(b)

To determine

To find: The limit if it exists.

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