Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to 1} \frac{x^3 - 2x^2 + 1}{x^3 - 1} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

This limit has the form $\frac{0}{0} . \quad \lim _{x \rightarrow 1} \frac{x^{3}-2 x^{2}+1}{x^{3}-1} \stackrel{\Perp}{=} \lim _{x \rightarrow 1} \frac{3 x^{2}-4 x}{3 x^{2}}=-\frac{1}{3}$Note: Alternatively, we could factor and simplify.

02:04

Mengsha Yao

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Campbell University

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

01:12

Find the limit. Use I'…

01:49

Find the limit. Use l'…

03:54

01:31

01:06

01:25

01:10

02:48

01:03

01:15

00:42

in this case we could use another method other than the hotel's rule. What we see is that it would give us actually in this case we would not be able to just give us the indeterminant form when we plug in X equals one. So because of that we want to look at the limit or the derivative of the numerator and the denominator now, so when we take the derivative, what we end up getting is three X squared minus for X. Provided by three x square. Now, when we plug in one, what we end up getting as a result Is going to be 3 -4 divided by free. So our final answer is going to be a negative one third. As a result, sometimes we can simplify it. So that way we don't have to use the hotel's rule, but in this case we have to use the hotel's role. Um and as long as we know how to take the derivative properly, it's fairly simple.

View More Answers From This Book

Find Another Textbook

01:40

The polynomial function f (x) is graphed below. Fill in the form below regar…

00:53

The function fx) is graphed. It represents translation of What equation repr…

03:12

An airplene sighied at the same lirne by two ground observers who are miles …

07:46

Factor each of the following polynomials.x" 166x2 _ Tx - 5R…

03:09

ASTAssigumem Question 5 marks) Sand is poured into right conical pile with t…

03:46

For what value of a is the following function continuous at every x?2x-=…

02:46

QUESTION 16 THE DISTRIBUTION OF INTELLIGENCE QUOTIENTs (IQs) OBTAINED FROMA …

02:30

(1 point)Two random samples are selected from two independent population…

02:31

A financial analyst has determined that there is a 235 probability that a mu…

05:06

Consider the partial differential equation a2 u au k ,k > 0 .By 8x2 ay us…