Which one of these is continuous at x=0?

[hangainlover]

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?

 

[Dustinsfl]

Someone has already taking the time to work on answering your question here.

http://www.mathhelpforum.com/math-help/calculus/138793-one-these-continuous-x-0-a.html