there an expression i had to show this function is continuos
$$ f(x) = \begin{cases} x\cdot \sin \frac1x,&x\neq 0 \\ 0,&x = 0 \end{cases} $$
while taking left hand limit or right hand
F(0-h) = $lt_{h→0}$ (0-h)(sin 1/(0-h))
in the next step i divided and multiplied sin function by 1/-h and i got answer 1 as $lt_{x→o}$sin(x)/x =1 Now that prove the function is discontinuous as Lhl ≠ limit at the point
Can anyone point where i am being wrong or what's wrong in my method. The question provided it's own answer , I'm just asking what's wrong with my method