   Chapter 9.2, Problem 7E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 3-8, determine whether each function is continuous or discontinuous at the given x-value. Examine the three conditions in the definition of continuity. f ( x ) = { x − 3  if  x ≤ 2 4 x − 7  if  x > 1 , x = 2

To determine

Whether the function, f(x)={x3     if x24x7   if x>2, is continuous or discontinuous at x=2.

Explanation

Given Information:

The provided function is f(x)={x3     if x24x7   if x>2.

Explanation:

Consider the provided function,

f(x)={x3     if x24x7   if x>2

A function, f, is continuous at x=c if f(c) exists, limxcf(x) exists and limxcf(x)=f(c).

The function is continuous at x=2 if all the three conditions are satisfied for x=2.

To check whether the value of f(2) exists, substitute 2 for x in the function,

f(2)=23=1

Thus, the value of f(4) is defined, which means the first condition is satisfied, and is equal to 1.

To check whether the limit, limx2f(x), exists, find the values of the left hand limit and the right hand limit. If the values of the left hand limit and right hand limit are equal, then the limit exists.

The limit from the left is represented by limx2f(x), that is, the values of f(2) but c<2

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