If `f(x)={x e^(-(1/(|x|)+1/x)),\ x!=0 , 0,\ x=0,\ t h e n\ f(x)` is a. Continuous as well as differentiable for all `x` b. Continuous for all `x` but not differentiable at `x=0` c. Neither differentiable nor continuous at `x=0` d. Discontinuous every where

If f(x)={xe^-(1/|x|+1/x) , x!=0 ,, 0, x=0 (1) discontinuous everywhere(2) continuous as well as differentiable for all x(3) continuous for all x but not differentiable at x=0(4) neither differentiable nor continuous at x = 0

If f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well as differentiable at x=0 continuous but not differentiable at x=0 differentiable but not continuous at x=0 none of these

If f(x)={(1)/(1+e^(1/x)),quad x!=00,quad x=0 then f(x) is continuous as well as differentiable at x=0 (b) continuous but not differentiable at x=0 (c) differentiable but not continuous at x=0 (d) none of these

show that f(x) =|x| is continuous but not differentiable at x =0

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function, is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

If f(x)={(1-cos x)/(x sin x),x!=0 and (1)/(2),x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (continuous but not differentiable (d)neither continuous nor differentiable

The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these

If f(x) ={ (x.ln(cosx))/ln (1+x^2) x!=0 , 0, x=0 then a) f is continuous at x =0 b) f is continuous at x =0 but not differentiable at x=0 c) f is differemtiable at x =0 d) f is not continuous at x =0