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if  f(x) =x for x≤ 0

             =0 for x >0 , then f(x) at x=0 is

Answer:

Explanation:

 Given ,   

 f(x) =x for x≤ 0

         =0 for x >0 

for continuity at x=0

 LHS at x=0   $\lim_{x \rightarrow 0^{-}}f(x)= \lim_{x \rightarrow0}x$

 $\lim_{h \rightarrow 0^{-}}(0-h)=0$ and RHL at x=0

 $\lim_{x \rightarrow 0^{+}} f(x)= \lim_{x \rightarrow 0^{+}} 0=0$

 Also, f(0)=0

 $\therefore$ LHL=RHL=f(0)

 Hence, f(x) is continuous at x=0

 For differentiability at x=0

 f'(x)=1 for x ≤  0, 0 for x >0

 $\therefore$   f(x) is not differentiable at x=0