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)={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

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

If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ 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

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)),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

The function f(x)=|cos sx| is everywhere continuous and differentiable everywhere continuous but not differentiable at (2n+1)(pi)/(2),n in Z .neither continuous not differentiable at (2x+1)(pi)/(2),n in Z

If f(x)=|3-x|+[3+x] , where [x] denotes the least integer greater than or equal to x , then f(x) is:(a) continuous and differentiable at x=3. (b) continuous but not differentiable at x=3. (c)differentiable but not continuous at x=3. (d)neither differentiable nor continuous at x=3..

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

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