   Chapter 2.4, Problem 61E

Chapter
Section
Textbook Problem

In Exercises 49-62, find the indicated limit, if it exists.61. lim x → 1 x − 1 x 3 + x 2 − 2 x

To determine
The limit of given expression if exists.

Explanation

Given information:

The given expression is limx1x1x3+x22x .

Calculation:

The given expression is shown below.

limx1x1x3+x22x

It is clearly seen from the above expression that the numerator and denominator approaches to zero as x approaches to 1 which means that the given expression is indeterminate form of (00) .

Factorize the above expression and cancel the common factors.

limx1x1x3+x22x=limx1x1x(x2+x2)=limx1(x1x(x2+2xx2))=limx1(x1x[x(x+2)1(x+2)</

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