29. Define functions f and g on [-1, 1] by f (x) = {* Cos(1/x), ifx #0; 0, and g(x) =0 cos(1/x), if x #0; if x = 0. if x = 0; Prove that f is continuous at 0 and that g is not continuous at 0. Explain why these functions are continuous at every other point in [-1, 1].
29. Define functions f and g on [-1, 1] by f (x) = {* Cos(1/x), ifx #0; 0, and g(x) =0 cos(1/x), if x #0; if x = 0. if x = 0; Prove that f is continuous at 0 and that g is not continuous at 0. Explain why these functions are continuous at every other point in [-1, 1].
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
![29. Define functions f and g on [-1, 1] by
f (x) = {* Cos(1/x), ifx # 0;
and
g(x) =
cos(1/x), if x # 0;
10,
0,
if x = 0;
if x = 0.
Prove that f is continuous at 0 and that g is not continuous at 0. Explain why these
functions are continuous at every other point in [-1, 1].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde096970-4fbf-4bcb-afca-efa41531f77d%2F8cd614c3-5a3e-4fe1-be96-511828d34b2a%2Frusi5pg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:29. Define functions f and g on [-1, 1] by
f (x) = {* Cos(1/x), ifx # 0;
and
g(x) =
cos(1/x), if x # 0;
10,
0,
if x = 0;
if x = 0.
Prove that f is continuous at 0 and that g is not continuous at 0. Explain why these
functions are continuous at every other point in [-1, 1].
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