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 21 Easy Difficulty

Evaluate the limit, if it exists.

$ \displaystyle \lim_{h \to 0}\frac{\sqrt{9 + h}-3}{h} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

DM
David Mccaslin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by David Mccaslin

Numerade Educator

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

More Answers

03:09

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
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

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 …

02:12

Use algebra to simplify th…

06:43

Find the indicated limit.<…

01:27

$11-32$ Evaluate the limit…

01:18

Use algebra to evaluate th…

02:41

Use algebra to evaluate th…

02:18

Find the limits.
$$\lim…

01:35

Find the limits.
$$\lim…

03:09

Evaluate the limit.
$$<…

01:40

Use algebra to simplify th…

0:00

Evaluate the limit, if it …

03:34

Evaluate the limit, if it …

0:00

Evaluate the limit, if it …

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

So in this problem were asked to determine the limits His age goes to zero of the squirt of nine plus H minus three. All over. H. All right. Notice that we can multiply this By the squirt of nine plus H plus three over itself. Because we can always multiply limit by one and still have the limit, right? Because one times anything is itself. So then this becomes the limit as h goes to zero of well nine plus the screwed at nine H minus three times. To scrutinize Jose plus three is just the first term squared minus the second term squared. So that means I end up with nine plus H- Well three square it is nine Over eight times the square root of nine plus H plus three. Okay, So this is the limit as h goes to zero of well 9 -9. That's those cancel out and H over the H then cancels out. Doesn't it? Let me let me do this one step at a time. So we're not getting confused here. So it's age over eight times The skirt of nine plus H. Was three. And now the H is canceled. So I'm left with limit As a church goes to zero of one over The square to nine plus H. Last three. Well as H goes to zero. Look at this the limit as H goes to zero. The screw nine plus H is simply what the screw to nine which is three. So this becomes 1/3 plus three which is 1/6. So our answer for this limit Is 1/6.

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
154
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
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

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_{h \to 0}\frac{\sqrt…

02:12

Use algebra to simplify the expression and find the limit. $$\lim _{h \rightarr…

06:43

Find the indicated limit. $$\lim _{h \rightarrow 0} \frac{\sqrt{3+h}-\sqrt{3}}{…

01:27

$11-32$ Evaluate the limit, if it exists. $$\lim _{h \rightarrow 0} \frac{\sqr…

01:18

Use algebra to evaluate the following limit...

02:41

Use algebra to evaluate the limits. $$\lim _{h \rightarrow 0} \frac{(-3+h)^{2}-…

02:18

Find the limits. $$\lim _{h \rightarrow 0} \frac{3}{\sqrt{3 h+1}+1}$$

01:35

Find the limits. $$\lim _{h \rightarrow 0} \frac{3}{\sqrt{3 h+1}+1}$$

03:09

Evaluate the limit. $$ \lim _{h \rightarrow 0} \frac{\sin 9 h}{h} $$

01:40

Use algebra to simplify the expression and find the limit. $$\lim _{h \rightarr…

0:00

Evaluate the limit, if it exists. $ \displaystyle \lim_{h \to 0}\frac{(x + h…

03:34

Evaluate the limit, if it exists. $$\lim _{h \rightarrow 0} \frac{(x+h)^{3}-x^…

0:00

Evaluate the limit, if it exists. $ \displaystyle \lim_{h \to 0}\frac{(2 + …
Additional Mathematics Questions

01:40

2. Suppose, you will be given 100, 000 pesos . Which of the following bank a…

01:55

Please I'm crying so hard rn because of the amount of activities
The…

00:37

if peter bought 3/4 kg of corn bitd and he repacked this into 1/8 kg each. H…

01:38

It takes Jon 16 hours 45 minutes to reach his home town from the city. If he…

01:35

let us help mang Kulas to find his lost carabao by going through the maze. f…

03:56

Problem solving involving Algebraic Expressions (answers with solution)
1…

05:41

Choose equivalent if the statement shows equivalency and not equivalent if t…

01:10

if gasoline cost 42.65 per liter and your gas tank holds 50.35 liters,then a…

01:01

The scores on a long test in Statistics follow a normal distribution with a …

00:55

find the product of 1 1/15 x 1 3/5 what a answers

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