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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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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