   Chapter 10.3, Problem 85E 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 75-88, identify all singular points of discontinuity of the given function, [HINT: See Example 3.] h ( x ) = { x + 2      if  x ≤ 0 0            if  x = 0 2 x + 2      if  x > 0

To determine

To calculate: The singular points and points of discontinuity of the function h(x)={x+2   if x<00         if x=02x+2 if x>0.

Explanation

Given Information:

The function is h(x)={x+2   if x<00         if x=02x+2 if x>0.

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxaf(x) exists and f(a) is defined, then

limxaf(x)=f(a)

The function is discontinuous at point x=a, if either,

a) The limit limxaf(x) does not exist or

b) The limit limxaf(x) does exist but it’s not equal to f(a).

Where, ‘a’ is any real number.

Calculation:

Consider the function h(x)={x+2   if x<00         if x=02x+2 if x>0

At x=0, the function changes from one closed-form to another. So, the point x=0 is the only possible point for discontinuity or a singular point.

Check at x=0 if the function is defined or not:

h(0)=0

At x=0 the function is equal to 0, which is defined.

Hence, it cannot be a singular point

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