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
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
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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