/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 37 In Problems 7鈥� 42, find each l... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q. 37 (page 883)

In Problems 7鈥� 42, find each limit algebraically.

limx鈫�1x3-x2+x-1x4-x3+2x-2.

Short Answer

Expert verified

The answer is23.

Step by step solution

01

Step. 1 Given Information

Firstly, we check whether the given function is in indeterminant form or not.

鈥�f(x)=x3-x2+x-1x4-x3+2x-2

Put x=1in the numerator we get,

x3-x2+x-1=1-1+1-1=0

Put x=1in the denominator we get,

x4-x3+2x-2=1-1+2-2=0.

Since both numerator and denominator gives 0 means they both have x=1as their common root.

02

Step. 2 Factorizing

Denominator,x4-x3+2x-2=x3(x-1)+2(x-1)=(x3+2)(x-1).

Numerator ,x3-x2+x-1=x2(x-1)+1(x-1)=(x2+1)(x-1).

So,

limx鈫�1x3-x2+x-1x4-x3+2x-2=limx鈫�1(x2+1)(x-1)(x3+2)(x-1)=limx鈫�1(x2+1)(x3+2).

Now we can put the limit directly.

03

Step. 3 Final calculation of the limit

limx鈫�1x2+1x3+2=1+11+2=23.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
limx鈫�2fx,fx=1

In Problems 7鈥� 42, find each limit algebraically

limx鈫�4x

In Problems 7鈥� 42, find each limit algebraically

limx鈫�-13x2-5x

In Problems 7鈥� 42, find each limit algebraically

limx鈫�-2(5x)

Graph each function. Use the graph to find the indicated limit, if it exists.limx鈫�4f(x),f(x)=3x
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.