   Chapter 9.2, Problem 4E ### 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. y = x 2 − 9 x + 3 , x = 3

To determine

Whether the function, y=x29x+3, is continuous or discontinuous at x=3.

Explanation

Given Information:

The provided function is y=x29x+3.

Explanation:

Consider the provided function,

y=x29x+3

Rewrite the function,

f(x)=x29x+3

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=3 if all the three conditions are satisfied for x=3.

To check whether the value of f(3) exists, substitute 3 for x,

f(3)=(3)293+3=996=06=0

Thus, the value of f(3) exists and is equal to 0

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