How do you differentiate #f(x) = x^2sin(1/x)#, when #f(x)# is defined as #0# for #x=0#?
1 Answer
You'll need to use the definition.
Explanation:
# = lim_(hrarr0)(f(h)-f(0))/h#
In this case we get
# = lim_(hrarr0)hsin(1/h)#
The limit hence, the derivative is
(Use the squeeze theorem.)
Bonus
An interesting thing about this function is that
Here is the graph of
graph{x^2sin(1/x) [-0.238, 0.2813, -0.095, 0.1643]}
Here's the graph of
graph{2xsin(1/x)+cos(1/x) [-1.865, 1.981, -0.872, 1.048]}