Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 11.2, Problem 56E
To determine

To Calculate : The limit, limx0f(x) by finding one-sided limits of the function, f(x). Also, draw the graph of the function such that f(x)={x2+3,x0x+5,x>0 .

Expert Solution & Answer
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Answer to Problem 56E

The limit, limx0f(x) does not exists . The graph of the function is given by,

  Precalculus with Limits: A Graphing Approach, Chapter 11.2, Problem 56E , additional homework tip  1

Explanation of Solution

Given information : The function is f(x)={x2+3,x0x+5,x>0 .

Formula used : If the left hand limit and right hand limits are equal then limxxf(x)=L otherwise the limits does not exists.

Calculation : When x0 , f(x) is given by x2+3 .

When x>0 , f(x) is given by x+5 .

Draw the graph of the function f(x).

  Precalculus with Limits: A Graphing Approach, Chapter 11.2, Problem 56E , additional homework tip  2

For left hand limit, substitute x=0 in the function, f(x)=x2+3 .

  limx0f(x)=limx0(x2+3)=(0)2+3=3

For right hand limit, substitute x=0 in the function, f(x)=x+5 .

  limx0+f(x)=limx0+(x+5)=(0)+5=5

As the left hand limit and right hand limit are not equal, the limit does not exists.

Chapter 11 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Prob. 60ECh. 11.1 - 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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY