Let f (x) = 1/x sin 1/x , for x not = 0.– Let xn = 1/n π^2. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.– Is f continuous at 0? Justify.– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?– Can f be redefined at 0 so that it’s continuous on R? Justify
Let f (x) = 1/x sin 1/x , for x not = 0.– Let xn = 1/n π^2. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.– Is f continuous at 0? Justify.– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?– Can f be redefined at 0 so that it’s continuous on R? Justify
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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Let f (x) = 1/x sin 1/x , for x not = 0.
– Let xn = 1/n π^2
. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.
– Is f continuous at 0? Justify.
– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)
as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?
– Can f be redefined at 0 so that it’s continuous on R? Justify
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