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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

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BuyFindarrow_forward

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
Chapter 13.2, Problem 40E
Textbook Problem
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Does the Limit Exist? Find the limit, if it exists. If the limit does not exist, explain why.

40. lim x 1.5 2 x 2 3 x | 2 x 3 |

To determine

To find: The value of limx1.52x23x|2x3|, if the limit exists.

Explanation of Solution

Given:

The limit is, limx1.52x23x|2x3|.

Calculation:

In the above limit, the function |2x3| is equal to 2x3 for 2x3>0.

2x3>0x>32x>1.5

So, the right-hand limit is,

limx1.52x23x|2x3|=limx1.5+2x23x2x3=limx1.5+x(2x3)2x3=limx1.5+x=1.5

The function |2x3| is equal to 2x+3 for 2x3<0

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Chapter 13 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - DISCUSS: A Function with Specified Limits Sketch...Ch. 13.1 - DISCUSS: Graphing Calculator Pitfalls (a)...Ch. 13.2 - Suppose the following limits exist:...Ch. 13.2 - If f is a polynomial or a rational function and a...Ch. 13.2 - Limits from a Graph The graphs of f and g are...Ch. 13.2 - Using Limit Laws Suppose that...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Evaluate the limit if it exists....Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Finding Limits Find the limit, and use a graphing...Ch. 13.2 - Does the Limit Exist? 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