Download the App!

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

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Evaluate the limit, if it exists. $ \displays…

View

Question

Answered step-by-step

Problem 20 Easy Difficulty

Evaluate the limit, if it exists.

$ \displaystyle \lim_{t \to 1}\frac{t^4 - 1}{t^3 - 1} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Ma. Theresa Alin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Ma. Theresa Alin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

03:42

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Related Topics

Limits

Derivatives

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Catherine Ross

Missouri State University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
Recommended Videos

0:00

Evaluate the limit, if it …

01:01

Evaluate the limit.
$$<…

00:49

Find the limit if it exist…

0:00

Evaluate the limit, if it …

0:00

Evaluate the limit, if it …

02:25

Evaluate the limit, if it …

03:12

Evaluate the limit, if it …

01:53

Evaluate the limit if it e…

0:00

Evaluate the limit, if it …

00:40

Evaluate the limit:
lim…

Watch More Solved Questions in Chapter 2

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66

Video Transcript

To evaluate this limit, we first rewrite teacher the 4th power -1. Overtake U -1. Since direct substitution gives us 1 to the 4th power -1 Over one K -1 which is just 0/0. An indeterminate value notes that T to the 4th power -1 over Take U -1. This is equal to t squared minus one times t squared plus one over T -1 times T squared plus t plus one. Which is the same as T -1 times t plus one times T squared plus one over t minus one times T squared plus t plus one. Now in here we can cancel out the T -1 and reduce the expression into T plus one times T squared plus one over T squared plus t plus one. And so using this we have this limit equal to limit as T approaches one of t plus one times t squared plus one over t squared plus t plus one which is just one plus one times one squared plus one over one squared plus one plus one, which is just 4/3. And so this is the value of the limit.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
143
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
Recommended Videos

0:00

Evaluate the limit, if it exists. $ \displaystyle \lim_{t \to 1}\frac{t^4 -…

01:01

Evaluate the limit. $$ \lim _{t \rightarrow 3}\left\langle t^{2}, 4 t, \frac{…

00:49

Find the limit if it exists. $$\lim _{t \rightarrow 1}\left\langle\sqrt{t-1}, t…

0:00

Evaluate the limit, if it exists. $ \displaystyle \lim_{t \to 0}\left( \frac…

0:00

Evaluate the limit, if it exists. $ \displaystyle \lim_{t \to 0}\left( \frac…

02:25

Evaluate the limit, if it exists. $\lim _{t \rightarrow 0}\left(\frac{1}{t}-\f…

03:12

Evaluate the limit, if it exists. $$\lim _{t \rightarrow 0}\left(\frac{1}{t}-\…

01:53

Evaluate the limit if it exists. $$ \lim _{t \rightarrow 0}\left(\frac{1}{t}-\f…

0:00

Evaluate the limit, if it exists. $ \displaystyle \lim_{t \to 0}\left( \frac…

00:40

Evaluate the limit: lim (t→ −1) 2t^2−4t=
Additional Mathematics Questions

02:10

A fruit merchant earns a profit of rs. 6 per bag oranges sold and a loss of …

01:09

By what rational number should 22/7 be Divided to get the number 11/24

02:22

10. Find the number which is: 53172 more than 64278 53172 less than 6427…

01:24

find three thousand one hundred thirty two added to thirty thousand and the …

02:34

write a quadratic polynomial whose zeros are 3-root2 and product of zeroes i…

08:24

An aircraft flies 400 km from a point O on a bearing of 025° and then 700 km…

01:46

a milkman has containers having capacity having capacity of 180 litres and 1…

03:24

Did you mean: if p and q are positive integers such as p>q prove that p2-…

01:45

a man sold his car for rupees 50000 loosing one tenth of its cost price find…

02:46

A house wife along with a group of ladies sold bags of different sizes. She …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started