F(x) = x * sin(1/x) for x =/=0 and f(0) = 0. continuous on R?

  • #1
squaremeplz
124
0

Homework Statement



Is the function f(x) = x * sin(1/x) for x =/= 0 and f(0) = 0 unifoirmly continuous on R?


Homework Equations





The Attempt at a Solution



dom(f) = (-inf, inf)



x,y in R and |x-y| < d imply |f(x) - f(y)| < e

|x - 0| < d imply |x * sin(1/x) - 0 | < e

?
 

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
2,017
4
f is continuous on R, and it looks like it has a bounded derivative on R\[-1,1].
 

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