Define f(x) to be zero when x=0.
Then
Sin(1/x) oscillates widly as x approaches zero; therefore, f'(0) does not exist.
But g'(0) =0.
Hello! I am having a lot of difficulty in terms of solving this problem, if anyone could help me that would be greatly appreciated. My teacher stated he would quiz us on this question, yet I have no clue how to approach it.
a) Set up the value of the function f(x)=xsin(1/x) at 0 to make it continuous. Then, by using the definition of the derivative, show that the new f is not differentiable at 0.
b) Determine whether the same is true for the function g(x)=x^2sin(1/x)-->after removing discontinuity at 0.
Thanks in Advance!