h(x)={x2sin(1x) if x≠00 if x=0
Is the derivative of h(x) continuous at x=0?
How about the derivative of k(x)=xh(x)?
When I tried to differentiate it directly, the cos(1/x) in the result suggests that the limit of h′(x) when x→0 does not exist.
However, when I use the definition to calculate the derivative, it shows that the derivative is 0 when x→0.
Which one is correct?
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