Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Problem 2
![Written HW
Problem 1:
Let (x) =
a) what is the domain of g(x)?
As you can see g(x) is defined when x=2 #0:
X will be greater than 2, 7.7.2, 1x-2) = x-2,
X-2
· g(x)= x - 2 = 7
X will also be less than 2, x < 2, 1x-21 = -(x-2) Pa
= -1
--(x-2).
(x-2).
: g(x) = 1
g(x) is defined as
(-∞02)0(2,00)
b) Use numerical method to find lim g(x) and lim g(x).
Using g(x)= x-21 to get closer to 1.
x-2
X-72+
X-2
"Z
જી।.૧૧૧૧) =
9 (2,001)=
X1.99 1.999 1.9999/2.0001|2.001
g(x)-1
-1
1 1 1
9(1.99) =
11.99-21-1-0.011 -0.01
-0.01 -0.01
1.99-2
11.9999-21 -0,000il
1.9999-2
-0.0001
12.001-21 -10.001t.
2.000-2
0.001
IX-21
X-2
-1
Plugging in our X's to get
our g(x).
11.999-21 1-0.0011:
1.999-2-0.001
1
= 1 12.0001-21_10.00011
2.0001-2
0.0001
limg(x) = -1 which is headed
to the left..
x+2-
|lim g(x) = 1 which is headed to
to right.
F
(calculate livec)
before
1
Based on my answer from (b) limg(x).
does NOT exist, DNE.
x42
We have figured out that limg(x) #lim g(x),
x-2-
x+27
which is a very big difference.
95
C) Based on your answer to (b), what is lim g(x)?
X-42
1
d) Sketch an accurate graph of g(x) on the interval.
[-4,4]. Be sure to include
any.
open
or close circles.
when plotting onto the graph it remains the same as
needed
Ix-21
but instead lies on 4.
X-2
45
15
65](https://content.bartleby.com/qna-images/question/a7110828-372e-4c54-bf93-fd3824e1823c/67da5a8c-e649-4c20-8261-a9b14348aa9a/ycmi1rj_processed.jpeg)
Transcribed Image Text:Written HW
Problem 1:
Let (x) =
a) what is the domain of g(x)?
As you can see g(x) is defined when x=2 #0:
X will be greater than 2, 7.7.2, 1x-2) = x-2,
X-2
· g(x)= x - 2 = 7
X will also be less than 2, x < 2, 1x-21 = -(x-2) Pa
= -1
--(x-2).
(x-2).
: g(x) = 1
g(x) is defined as
(-∞02)0(2,00)
b) Use numerical method to find lim g(x) and lim g(x).
Using g(x)= x-21 to get closer to 1.
x-2
X-72+
X-2
"Z
જી।.૧૧૧૧) =
9 (2,001)=
X1.99 1.999 1.9999/2.0001|2.001
g(x)-1
-1
1 1 1
9(1.99) =
11.99-21-1-0.011 -0.01
-0.01 -0.01
1.99-2
11.9999-21 -0,000il
1.9999-2
-0.0001
12.001-21 -10.001t.
2.000-2
0.001
IX-21
X-2
-1
Plugging in our X's to get
our g(x).
11.999-21 1-0.0011:
1.999-2-0.001
1
= 1 12.0001-21_10.00011
2.0001-2
0.0001
limg(x) = -1 which is headed
to the left..
x+2-
|lim g(x) = 1 which is headed to
to right.
F
(calculate livec)
before
1
Based on my answer from (b) limg(x).
does NOT exist, DNE.
x42
We have figured out that limg(x) #lim g(x),
x-2-
x+27
which is a very big difference.
95
C) Based on your answer to (b), what is lim g(x)?
X-42
1
d) Sketch an accurate graph of g(x) on the interval.
[-4,4]. Be sure to include
any.
open
or close circles.
when plotting onto the graph it remains the same as
needed
Ix-21
but instead lies on 4.
X-2
45
15
65
![4:04
MAT 131 Written HW Sec...
M
MAT 131-Applebee
Written HW-Sections 1.2 and 1.3
You may collaborate with up to 3 other students on written HW assignments -no collaboration
across groups. You may not work with a tutor or upload this assignment to a site like Chegg.
Your final submission should be your own work, explained in your own words. To submit the
assignment, either scan your written work as a PDF (GeniusScan is a free scanning app) or type
your work and save it as PDF to upload. Be sure to review the Written HW Guidelines and
Expectations in the Syllabus before submitting your assignment.
Problem 1:
Let (x) =
|x-21
x-2
a) What is the domain of g(x)?
b) Use numerical methods to find lim g(x) and lim g(x).
c) Based on your answer to (b), what is lim g(x)? Write at least one sentence to explain
how you determined this limit.
d) Sketch an accurate graph of g(x) on the interval [-4,4]. Be sure to include any needed
open or closed circles.
Problem 2:
The goal of this problem is to compute the value of the derivative at a point for two different
functions. You will compute the limit in three different ways and then compare the results to
see that each produces the same value.
For each of the following functions, use the following 3 methods to compute the derivative at
point a.
Dashboard
1. Use the limit definition of the derivative (algebraic)
2. Use a numerical approach (with at least 2 small values of h)
3. plot the graph near a, along with the appropriate tangent line to estimate the value of
f'(a) visually.
After to have computed the limit all 3 ways, write at least one sentence comparing the results.
Function 1
Function 2
f(x) == at a = 1
f(x) = x² - 4x at a = 3
а
BY SA
https://activecalculus.org/single/sec-1-2-lim.html
https://activecalculus.org/single/sec-1-3-derivative-pt.html
Calendar
8
To Do
©2012-2019 Matthew Boelkins
A
Notifications
1
Inbox](https://content.bartleby.com/qna-images/question/a7110828-372e-4c54-bf93-fd3824e1823c/67da5a8c-e649-4c20-8261-a9b14348aa9a/18d7e08_processed.jpeg)
Transcribed Image Text:4:04
MAT 131 Written HW Sec...
M
MAT 131-Applebee
Written HW-Sections 1.2 and 1.3
You may collaborate with up to 3 other students on written HW assignments -no collaboration
across groups. You may not work with a tutor or upload this assignment to a site like Chegg.
Your final submission should be your own work, explained in your own words. To submit the
assignment, either scan your written work as a PDF (GeniusScan is a free scanning app) or type
your work and save it as PDF to upload. Be sure to review the Written HW Guidelines and
Expectations in the Syllabus before submitting your assignment.
Problem 1:
Let (x) =
|x-21
x-2
a) What is the domain of g(x)?
b) Use numerical methods to find lim g(x) and lim g(x).
c) Based on your answer to (b), what is lim g(x)? Write at least one sentence to explain
how you determined this limit.
d) Sketch an accurate graph of g(x) on the interval [-4,4]. Be sure to include any needed
open or closed circles.
Problem 2:
The goal of this problem is to compute the value of the derivative at a point for two different
functions. You will compute the limit in three different ways and then compare the results to
see that each produces the same value.
For each of the following functions, use the following 3 methods to compute the derivative at
point a.
Dashboard
1. Use the limit definition of the derivative (algebraic)
2. Use a numerical approach (with at least 2 small values of h)
3. plot the graph near a, along with the appropriate tangent line to estimate the value of
f'(a) visually.
After to have computed the limit all 3 ways, write at least one sentence comparing the results.
Function 1
Function 2
f(x) == at a = 1
f(x) = x² - 4x at a = 3
а
BY SA
https://activecalculus.org/single/sec-1-2-lim.html
https://activecalculus.org/single/sec-1-3-derivative-pt.html
Calendar
8
To Do
©2012-2019 Matthew Boelkins
A
Notifications
1
Inbox
Expert Solution
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Step 1
Question number 2. contains two different functions so I solve the problem for first function. For other repost it.
Trending nowThis is a popular solution!
Step by stepSolved in 5 steps with 5 images
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