Is every differentiable function continuous?

Is every invertible function monotonic?

If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than or equal to x , then f(x) is continuous and differentiable at x=3 continuous but not differentiable at x=3 differentiable but not continuous at x=3 neither differentiable nor continuous at x=3

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..

Show that every polynomial function is continuous.

Prove that every rational function is continuous.

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)={(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

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)=(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