(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Limit problem using the formal definition of a derivative

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