   Chapter 10.2, Problem 40E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 33–42, use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. [HINT: See Example 1.] f ( x ) = { 1 x 2       if  x ≠ 0 0            if  x = 0

To determine

Whether the function h(x)={1x2, if x02, if x=0 is continuous on its domain using the graph and give the points of discontinuity if it is not continuous on its domain.

Explanation

Given information:

The provided function is h(x)={1x2, if x02, if x=0.

Consider the function, h(x)={1x2, if x02, if x=0

To draw the graph of h(x)={1x2, if x02, if x=0, first compute the value of h(x) for different values of x.

Compute the value of h(x) at x=1 by substituting x=1 in the equation h(x)=1x2 as,

h(1)=1(1)2=1

Compute the value of h(x) at x=1 by substituting x=1 in the equation h(x)=1x2 as,

h(1)=1(1)2=1

Compute the value of h(x) at x=2 by substituting x=2 in the equation h(x)=1x2 as,

h(2)=1(2)2=14

Compute the value of h(x) at x=2 by substituting x=2 in the equation h(x)=1x2 as,

h(2)=1(2)2=14

Thus, the ordered pairs formed are,

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