   Chapter 2, Problem 29RE

Chapter
Section
Textbook Problem

In Exercises 27–30, determine all values of x for which each function is discontinuous.29. f(x) = { 1 ( x + 1 ) 2  if   x    ≠   − 1 2     if   x   =   − 1

To determine
The value of x at which the given function is discontinuous.

Explanation

Given:

The function is f(x)={1(x+1)2ifx12ifx=1 (1)

Definition used:

The function will be continuous when the value of left hand limit and the value of right hand limit is equal to the value of the function at that point and value of that function should satisfy that point.

A function f is continuous at x=a when it follows the following three conditions,

(1) f(a) is defined.

(2) limxaf(x) exists.

(3) limxaf(x)=f(a)

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