If `[.]` and `{.}` denote greatest and fractional part functions respectively and `f(x)={(x((e^([x]+|x|)-2)/([x]+{2x})),x!=0),(-1,x=0):}` then (A) `f(x)` is differentiable every where (B) `f(x)` is continuous at `x=0` (C) `f(x)` is continuous every where (D) `f(x)` is not differentiable at `x=0`

If f(x)=x^3(sgn [x] + {x}):0le xlt2, cosx+|x-2| ; 2 le x le pi Where [.], {.} and sgn (.) represents the greatest integer, the fractional part and signmum function respectively A. f(x) is differentiable at x = 1 B) f(x) is continuous but non-differentiable at x = 1 C) f(x) is discontinuous at x= 2 D) f(x) is non-differentiable at x =2

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

If f(x) = [x^2] + sqrt({x}^2 , where [] and {.} denote the greatest integer and fractional part functions respectively,then

The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (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

Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is continuous but not differentiable at x=0 . If

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x=0

The function f(x)=sin^(-1)(cosx) is (a) . discontinuous at x=0 (b). continuous at x=0 (c) . differentiable at x=0 (d) . non of these

Let f(x)={(x(e^([x]+x)-4)/([x]+|x|), , x!=0),(3, , x=0):} Where [ ] denotes the greatest integer function. Then,

Show that the function f(x)=2x-|x| is continuous at x=0.