Let `f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0`, test the continuity & differentiability at `x = 0`

Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x) is differentiable at x=0

If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not differentiable at x = 0

Let f(x) = (x+|x|)/x for x ne 0 and let f (0) = 0, Is f continuous at 0?

Let , f(x)=1/xsin(x^2) when x ne0 =0 when x=0 Discuss the continuity and differentiability of f(x) at x=0.

Let f(x)={(x^(p)"sin"1/x,x!=0),(0,x=0):} then f(x) is continuous but not differentiable at x=0 if

If f(x)={xe^(-[(1)/(|x|)+(1)/(x)]);x!=0;0;x=0 Prove that f(x) is not differentiable at x=0