f(0)=0;f(x)=xe−(∣x∣1+x1) R.H.L. h→0lim(0+h)e−2/h=h→0lime2/hh=0 L.H.L Limh→0(0−h)e−(h1−h1)=0 Therefore, f(x) is continuous R.H.D. h→0limh(0+h)e−(h1+h1)−he−(h1+h1)=0 L.H.D. Limh→0−h(0−h)e−(h1−h1)−he−(h1+h1)=1 Therefore, L.H.D. = R.H.D. f(x) is not differentiable at x=0.