Limit problem using the formal definition of a derivative

[oates151]

Homework Statement

Use the definition of the derivative to determine if f'(0) exists for the function,

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

Homework Equations

f'(x) = f(x+h) - f(x)
------------
h

The Attempt at a Solution

Starting plugging it all in as usual and got to

(x^2 +2xh + h^2)(sin(1/x+h)) - (x^2)(sin(1/x)
----------------------------------------------
h

How do I simplify from here?

Thanks in advance - I really want to develop a solid method to solving these.

 

[micromass]

You're doing it too general know. That is, you're forming the quotient

$$\frac{f(x+h)-f(x)}{h}$$

But here you know that x=0. So try form the quotient where x=0.