# Limit problem using the formal definition of a derivative

1. Sep 28, 2011

### oates151

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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 wanna develop a solid method to solving these.

2. Sep 28, 2011

### micromass

Staff Emeritus
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.