   Chapter 10.3, Problem 110E 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

Give examples of two limits: one that leads to a determinate form and another that leads to an indeterminate form but where neither limit exists.

To determine

The example of two limits where one limit is indeterminate form and the other one is in indeterminate form and both limits do not exist.

Explanation

Consider the limit limx11x1.

Now, apply continuity of closed-form theorem limxaf(x)=f(a):

limx11x1=1(1)1=111=10

Here, 10 is the determinate form.

Now, check whether the limit exists or not:

Consider the right limit:

limx1+f(x)=limx1+1x1

Apply continuity of closed-form theorem limxaf(x)=f(a):

limx1+1x1=11+1=10+=+

Consider the left limit:

limx1f(x)=limx11x1

Apply continuity of closed-form theorem limxaf(x)=f(a):

limx11x1=11+1=10=

The left and right limits are not equal.

Hence, the limit does not exist.

Now, consider the limit, limx2x2(x2)2

Apply continuity of closed-form theorem limxaf(x)=f(a):

limx2x2(x2)2=22((2)2)2=0(22)2=00

Here, 00 is the indeterminate form

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 