   Chapter 1.7, Problem 19E

Chapter
Section
Textbook Problem

Prove the statement using the ε , δ definition of a limit. lim x → 1 2 + 4 x 3 = 2

To determine

To Show:

limx12+4x3=2

Explanation

1) Concept:

Let f be function defined on some open interval that contains the number  a, except possibly at a itself. Then we say that the limit of f(x) as x approaches a is L, and we write

limxafx=L

If for very ϵ>0 there is a number δ>0 such that

If 0<x-a< δ  then fx-L< ϵ.

2) Calculations:

Here we have fx= 2+4x3, L=2  and  a=1.

By  ϵ, δ  definition for given  ϵ  we have to find δ.

If 0<x-1< δ  then 2+4x3-2<  ϵ

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