$ f(x) = \begin{cases} \frac{sin(x)}{x}, & x \ne0 \\ x+1, & x=0 \end{cases}$
I know that the function is a continuous function in R. But is this function derivable at x=0?
I am not sure..
Thanks
2026-04-05 19:35:49.1775417749
is split function derivable
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RHS: lim$_{h\rightarrow 0}\dfrac{f(h)-f(0)}{h}=\dfrac{\sin h-h}{h^2}$
On applying L'Hospital's Rule twice we get limit 0
Similarly LHS:
$\dfrac{f(0)-f(-h)}{h}=\dfrac{h-\sin h}{h^2}(\dfrac{0}{0})$
On applying L'Hospital's Rule twice we get limit 0
Thus differentiable at 0