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

If f(x) = x^(3) sgn (x), then A. f is differentiable at x = 0 B. f is continuous but not differentiable at x = 0 C. f'(0^(-)) = 1 D. None of these

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

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+{-x}+[x] , where [x] and {x} denotes greatest integer function and fractional part function respectively, then find the number of points at which f(x) is both discontinuous and non-differentiable in [-2,2] .

If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R^+, the set of positive real numbers, and f(x)={[g(x)],x(0,pi/2)uu(pi/2,pi) and 3,x=pi/2 where [.] denotes greatest integer function. Then (a) f(x) is continuous and differentiable at x=pi/2, when 0ltnlt1 (b) f(x) is continuous and differentiable at x=pi/2, when ngt1 (c) f(x) is discontinuous and non differentiable at x=pi/2,for0ltnlt1 (d) f(x) is continuous but not differentiable at x=pi/2, when ngt1

Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2 .

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then continutity and diffrentiability of f(x)

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) ={{:( xe^(x), xle0),( x+x^(2)-x^(3), xgt0):} then the correct statement is (a) f is continuous and differentiable for all x (b) f is continuous but not differentiable at x=0 (c) f is continuous and differentiable for all x . (d) f ' is continuous but not differentiable at x=0

Discuss the differentiability of f(x) =x[x]{x} in interval [-1,2] , where [.] and {.} denotes the greatest integer function and fractional part fntion , respectively .