   Chapter 1.5, Problem 9CP

Chapter
Section
Textbook Problem

Find the limit of f ( x ) as x approaches 0. f ( x ) = { x 2 + 1 ,    x  < 0 2 x + 1 ,    x > 0

To determine

To calculate: The limit of the function f(x)={x2+1,      x<02x+1,      x<0 as x approaches to 0.

Explanation

Given information:

The function is f(x)={x2+1,      x<02x+1,      x<0.

Formula used:

Notation for a limit:

limxcf(x)=L

The above expression is represented as, “the limit of f(x) as x approaches c is L.”

Calculation:

Consider the provided function, f(x)={x2+1,      x<02x+1,      x<0.

The provided function breaks at point 0, so calculate the value of f(x) near point x=0.

For x<0

The function is f(x)=x2+1.

The limit from the left to 0 for the function is given as,

limx0f(x)=limx0(x2+1)=(0)2+1=1

For x>0

The function is f(x)=2x+1.

The limit from the right to 0 for the function is given as,

limx0+f(x)=limx0+(2x+1)=2(x)+1=2+1=3

Now, both side limit of the function exists and equal to 1.

limx0+f(x)=limx0f(x)

Substitute 0 for x in either function f(x)=x2+1.

f(0)=x2+1=02+1=1

Now, choose some values for x and compute the value for f(x), in order to form the ordered pairs that will plot on the graph

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