   Chapter 10.3, Problem 40E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 21-74, calculate the limit algebraically. If the limit does not exit, say why, lim x → 0 + 1 x 2 − x [HINT: See Example 2.]

To determine

To calculate: The value of limx0+1x2x algebraically and give reason, if limit does not exist.

Explanation

Given Information:

The provided limit is limx0+1x2x.

Formula used:

The determinate form is as follows:

k0±=±

Where, k is any constant. And, the form 00 and± are indeterminate form.

Calculation:

Consider the limit,

limx0+1x2x

The function f(x)=1x2x is a closed-form function, x=0 is a singular point.

Now, substitute x=0 in the function f(x)=1x2x;

1x2x=1(0)2(0)=10

It has the determinate form k0.

For the limit limx0+1x2x, x is approaching 0 from the right, so the denominator x(x1) is negative

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