(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Limit problem using the formal definition of a derivative

**Physics Forums | Science Articles, Homework Help, Discussion**