Consider the function defined by f(x) = -(x + 1)² +5 if x < 0 x +4 if 0 ≤ x ≤4 1/(x − 3) if x > 4 Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer by addressing all the conditions for continuity.
Consider the function defined by f(x) = -(x + 1)² +5 if x < 0 x +4 if 0 ≤ x ≤4 1/(x − 3) if x > 4 Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer by addressing all the conditions for continuity.
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
![Consider the function defined by
f(x) =
-(x + 1)² +5 if x < 0
x +4
if 0 ≤ x ≤ 4
1/(x-3)
if x > 4
Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer
by addressing all the conditions for continuity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b421daf-4b57-4fe1-ad05-03b7cb5ea3bb%2Fab0d3a9f-78ab-4b89-98c2-9444fdb15ce9%2Fawe9sk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function defined by
f(x) =
-(x + 1)² +5 if x < 0
x +4
if 0 ≤ x ≤ 4
1/(x-3)
if x > 4
Graph the function. Is the function continuous at x = 0 and x = 4? Justify your answer
by addressing all the conditions for continuity.
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