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

(a) If the symbol [] I denotes the greatest integ…

05:29

Question

Answered step-by-step

Problem 52 Hard Difficulty

Let
$ g(x) = \left\{
\begin{array}{ll}
x & \mbox{if $ x < 1 $}\\
3 & \mbox{if $ x = 1 $}\\
2 - x^2 & \mbox{if $ 1 < x \le 2 $}\\
x - 3 & \mbox{if $ x > 2 $}
\end{array} \right.$

(a) Evaluate each of the following, if it exists.

(i) $ \displaystyle \lim_{x \to 1^-}g(x) $
(ii) $ \displaystyle \lim_{x \to 1}g(x) $
(iii) $ g(1) $
(iv) $ \displaystyle \lim_{x \to 2^-}g(x) $
(v) $ \displaystyle \lim_{x \to 2^+}g(x) $
(vi) $ \displaystyle \lim_{x \to 2}g(x) $

(b) Sketch the graph of $ g $.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Daniel Jaimes
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Daniel Jaimes

Numerade Educator

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

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

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

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

03:05

Let
$$g(x)=\left\{\begi…

01:17

Let
$$g(x)=\left\{\begi…

05:11

Let
$$g(x)=\left\{\begi…

05:36

Let
if x < 1 if * =1…

03:25

Sketch the graph of $$g(x)…

02:58

Sketch the graph of $f(x)=…

04:06

(a) Graph the function $g$…

03:23

Sketch the graph of $f(x)=…

08:37

Sketch the graph of $f(x)=…

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

This is problem or fifty two of the Stuart Calculus eighth edition Section two point three Let GM Back sequel This piece wise function made up of the first function. X if X is less than one in second function. Three. If X is equal to one, but their function to minus X squared, if one is less than X, is less than or equal to two in the last function, X minus three. If X is greater than two, evaluate each of the following If it exists part one of party The limit is X approaches one from the left of Jean. So as we approach one from the left, we are only concerned with the first function as we have not yet reached one, at which point we would switch to the second function Her for our solution to problem. Part one is that as we approach one from the left, we stay with this function and as we approach one, X equals one. The limit is equal to one part two limited expertise one no gene and then we have to look at both the left and the right. Lim left, left, left and we already solved in part one for the rec limit. We have to use this function here because this is where we are. Protein IX from the rate of one two x is greater than one. In this case, as we approach one two minus X squared approaches to minus one squared or one. So since the limit and six approaching, a warning from the rain is equal to warn her G is equal to one, and that would limit from the left is also equal to one. Then we say that the limit insects that produced one from G is equal to one. They both exist on their people to one what is G of one alone? Part three. We need to look at where X is equal to one. And there is this function on the value of the function at X equals one and says here is exactly equal to three. Her answer from birth three history part for the limiters. Expressions too. From the left of the function G, we look at which part of the function that coincides with here we're here. X is less than or equal to two. This will be the function as we approached two from the left. The function to minus X squared as we approach, too, should be two minus two squared or two minus four, which is equal to negative, too. Pipe part time. The limit is expertise to from the right of tea means that we have to look at the last function here since we're looking at, numbers are the largest them, too, as we approach, too, Disfunction expended three approaches a negative one, and so that is our limit for part five. Part six. Part six takes A look at the limit is he poached you from the left and the limited. He put Steven right Tina's although they both exist, but they have different values. We say that tournament, crying the limit of Part six, does not exist for the reason that limits from the left as you approach two does not equal delimit from the right. As he approached you finally, per p sketched the rest of the function. Here we have a plant showing each part X when X is less than one that is a straight line with the soul of one at X equals one. We ever Valley of three shown appear between one two. We have a new function to minus X squared, which is a downward facing problem. And then we see here that there's a jump provided that the limit is onyx. Aesthetics equals two where the function afterward is X minus three, and this is a graph of the function.

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
177
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
75
Hosted by: Alonso M
See More

Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

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

03:05

Let $$g(x)=\left\{\begin{array}{ll}{x} & {\text { if } x < 1} \\ {3} & {\text …

01:17

Let $$g(x)=\left\{\begin{array}{ll} x & \text { if } x < 1 \\ 3 & \text { if…

05:11

Let $$g(x)=\left\{\begin{array}{ll}{x} & {\text { if } x < 1} \\ {3} & {\text …

05:36

Let if x < 1 if * =1 if 1 <* s 2' X - 3 ifx> 2 g(X) (a) Evaluate each of the fo…

03:25

Sketch the graph of $$g(x)=\left\{\begin{aligned}-x+1 & \text { if } x<1 \\x-1 …

02:58

Sketch the graph of $f(x)=\left\{\begin{array}{lll}x^{2}+1 & \text { if } & x<-…

04:06

(a) Graph the function $g$ whose rule is $$g(x)=\left\{\begin{array}{ll}x^{2} &…

03:23

Sketch the graph of $f(x)=\left\{\begin{array}{lll}2 x+1 & \text { if } & x<-1 …

08:37

Sketch the graph of $f(x)=\left\{\begin{array}{ll}x^{3}-1 & \text { if } \quad …
Additional Mathematics Questions

01:44

QUESTIon 5
How much did Gloria invest 6.1 years ago at 3.384 compounded q…

00:52

In this problem WC will study tests that might be poorly designed: Consider …

01:54

(a) z = -1.17 for a left tail test for a mean
Round your answer to three …

02:28

prove they are the same
A U (B _ (An B)) U (C _ (Au B) )
=
P(A) + P…

02:43

Consider the bases B = {u1; U2} and B' = {v1, V2} for R2 where U1 = [d7…

01:54

191
Uring tho graph ofy = sin x, Iist a4 values on tha intorvil
sabaly…

01:10

Using naive forecasting method, the forecast for next month'$ sales vol…

06:05

Contider the DE / Pely" 1*1"0, Ezx8n886 baln ehor cfontinuor = on …

03:35

A bookcase is to have 4 shelves including the top as pictured below:
The …

02:22

6 (4 8.4.43 complete} Ioa dimensions of home plate at a random home plato; b…

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