Which one of these is continuous at x=0?

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Homework Statement



1) f(x) = sin(1/x) for x is not 0
= 0 for x is 0
2) f(x) = x sin (1/x) for x is not 0
=0 for x = 0


Homework Equations





The Attempt at a Solution


i've got a hunch the answer is the second one
(i think that factor 'x' is going to minimize the total value when x is really close to 0 )

but i can't find a mathmatical way of looking at it..
any help?
 
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