   Chapter 1.2, Problem 48E ### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

#### Solutions

Chapter
Section ### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Using the ε − δ Definition of Limit In Exercises 45-56, find the limit L. Then use the ε − δ definition to prove that the limit is L. lim x → − 3 ( 3 4 x + 1 )

To determine

To calculate: The value of limit L of a function limx334x+1 and proving the result by εδ definition.

Explanation

Given:

limx334x+1

limx334x+1=94+1=134

Calculation:

εδ definition states that if ε>0,thenthereexistsapostive integer δ>0 such that |f(x)L|<ε,whenever0<|xc|<δ ——–(1)

Substituting f(x)=34x+1,L=134,andc=3instatement(1),weget

|34x+1134|<εwhenever0<|x3|<δ

|3x94|<

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