   Chapter 10.3, Problem 38E 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 → − 2 x 3 + 8 x 2 + 3 x + 2

To determine

To calculate: The value of the limit limx2x3+8x2+3x+2 algebraically and give reason, if limit does not exist.

Explanation

Given Information:

The provided limit is limx2x3+8x2+3x+2.

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxaf(x) exists and f(a) is defined, then

limxaf(x)=f(a)

The sum of cubes is represented as:

(a3+b3)=(a+b)(a2ab+b2)

Calculation:

Consider the limit,

limx2x3+8x2+3x+2

Now, x3+8x2+3x+2 is a closed-form function, but x=2 does not lie within its domain.

So, continuity of closed form theorem cannot be applied.

Try to simplify the limit:

limx2x3+8x2+3x+2=limx2x3+(2)3x2+3x+2

Apply sum of cubes and factorize the equation:

limx2x3+(2)3x2+3x+2=limx2(x+2)(x22x+(2)2)x2<

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

Prove that ddx(cotx)=csc2x.

Single Variable Calculus: Early Transcendentals, Volume I

Finding Derivatives In Exercises 51-62, find f(x). f(x)=x22x2x4

Calculus: An Applied Approach (MindTap Course List)

Find the value of the sum. 30. i=1n(25i)

Single Variable Calculus: Early Transcendentals

A number c that satisfies the Mean Value Theorem for f(x) = x3 on [1, 4] is: a) 7 b) 12 c) 63 d) 63

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 