Consider the piecewise function 2+x² x<0 x=0 g(x) = 1, 2-³, 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Consider the piecewise function
2+x2 <0
x = 0
2 – a3, 0 <x <1
1,
g(x) =
2 - x
x 21
(a) For each of the values of r = 0, and 1, discover whether g(x) is continuous
using the continuity test. Without carrying out any further calculation,
what can you conclude about the differentiability at point r = 0?
(b) Sketch the graph of f(r) and test the differentiability of the function at
the at the point x = 1.
Transcribed Image Text:1. Consider the piecewise function 2+x2 <0 x = 0 2 – a3, 0 <x <1 1, g(x) = 2 - x x 21 (a) For each of the values of r = 0, and 1, discover whether g(x) is continuous using the continuity test. Without carrying out any further calculation, what can you conclude about the differentiability at point r = 0? (b) Sketch the graph of f(r) and test the differentiability of the function at the at the point x = 1.
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