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

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)=|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..

The function f(x)=e^(|x|) is (a) Continuous everywhere but not differentiable at x = 0 (b) Continuous and differentiable everywhere (c) Not continuous at x = 0 (d) None of the above

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function,(a) 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

Show that the function f(x)=2x-|x| is continuous but not differentiable at x=0

If f(x)={e^(1//x),\ \ \ if\ x!=0 1,\ \ \ if\ x=0 . Find whether f is continuous at x=0

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function, (a) 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

The function f(x)=1+|cosx| is (a) continuous no where (b) continuous everywhere (c) not differentiable at x=0 (d) not differentiable at x=npi,\ \ n in Z

The function f : R rarr R given by f(x) = - |x-1| is (a) continuous as well as differentiable at x = 1 (b) not continuous but differentiable at x = 1 (c) continous but not differentiable at x = 1 (d) neither continous nor differentiable at x = 1