-ម៉ា- I0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Practice with Continuity
Consider the graphed piecewise function f (x) shown below.
• Determine the open intervals on which f (x) is continuous.
Determine, for the values x = −2, x = 0, x = 1, x = 3, x = 4, and x =
●
o Continuous;
o Left-continuous;
o Right-continuous.
• For each value that ƒ (x) has a discontinuity, state:
o Which type of discontinuity it is;
o Which of the three criteria for continuity are and are not met.
Guiding Discussion Questions:
What are the three criteria for continuity?
• How is continuity/discontinuity apparent on a graph? How is this related to using a graph to evaluate limits?
• How is one-sided continuity related to one-sided limits?
●
-5
-5-
0
-5-
5, for which values ƒ (x) is:
10
Transcribed Image Text:Now consider the equation for the function above:
2x + 3,
-x² +3,
f(x) =
-2x+2,
1
²¹²3 + ²/ ,
x-3
●
1
x-3'
x<-2
-2 ≤ x < 0
0 < x < 1
1<x<3
3 < x < 4, x > 4
X = 4
2,
Use the equation and the limit definitions of one-sided and two-sided continuity to verify the conclusions you drew from
the graph regarding continuity and discontinuity at each point.
Guiding Discussion Questions:
• What are the three criteria for continuity?
• What limits do we write down to algebraically show that the function is or is not continuous at each point?
How is one-sided continuity related to one-sided limits? How do we write these to verify algebraically what we
found on the graph?
How do we decide which "piece" of the function rule to use at each step?
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