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

[squaremeplz]

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

?

 

[morphism]

f is continuous on R, and it looks like it has a bounded derivative on R\[-1,1].