5. Use f(r) = r? - 3|r| to answer the following questions (a) Sketch an accurate graph of f(x) in the axes below. [An domain, has the correct shape, and key points on the (Hint: Once vou sketch a rough graph double check it w
5. Use f(r) = r? - 3|r| to answer the following questions (a) Sketch an accurate graph of f(x) in the axes below. [An domain, has the correct shape, and key points on the (Hint: Once vou sketch a rough graph double check it w
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![5. Use f(x) = r² – 3|r| to answer the following questions
(a) Sketch an accurate graph of f(x) in the axes below. [An accurate graph shows the function's
domain, has the correct shape, and key points on the graph have the corTect coordinates.]
[Hint: Once you sketch a rough graph, double check it with Desmos.]
thie
(b) L1 I can determinc the points at which a function is (and is not) continuous both graphically
and algebraically.
Where, if anywhere, is f(x) discontinuous?
(c) T1 I can apply mathematical definitions. Use the limit definition of continuity to determine
if f(r) is continuous when r = 0.
W1S NOT
7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8dc01d7-4edf-4516-bda1-b59df0529e79%2F21857526-a727-4fec-b395-a016129e9d9c%2Ffnugv7i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Use f(x) = r² – 3|r| to answer the following questions
(a) Sketch an accurate graph of f(x) in the axes below. [An accurate graph shows the function's
domain, has the correct shape, and key points on the graph have the corTect coordinates.]
[Hint: Once you sketch a rough graph, double check it with Desmos.]
thie
(b) L1 I can determinc the points at which a function is (and is not) continuous both graphically
and algebraically.
Where, if anywhere, is f(x) discontinuous?
(c) T1 I can apply mathematical definitions. Use the limit definition of continuity to determine
if f(r) is continuous when r = 0.
W1S NOT
7.
Transcribed Image Text:When a = 0, f(x) IS/ IS NOT continuous, and f(x) IS/ IS NOT differentiable. (Circle the correct
(a) DI I can use the limit definition of the derivative to determine the differentiability of a
function at a point.
The limit definition of the derivative at a point is:
pant ob
f(a+ h) - f(a)
f'(a) = lin
(6 Using the definition above, determine if f'(0) exists if f (x) = x² – 3|x|. (Please save yoursell
and the grader a lot of trouble by using the definition with a and NOT . Hint: a = 0 for this
problem-use tlhis fact as soon as possible. Also, please remember how to deal with absolute
values and limits.)
responses.)
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