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+{-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] .

f(x)={(x[x],if 0 le x< 3),((x-1)[x],if 3lexle4)) where [x] is the greatest integer function. The function f(x) is (A) continuous and differentiable at x=3 (B) continuous at x=1,2,3 (C) continuous but not differentiable at x=3 (D) discontinuous at x=1,2,3

If f(x)={x^2(sgn[x])+{x},0 <= x <= 2 sin x+|x-3| ,2 < x< 4 , (where[.] & {.} greatest integer function & fractional part functiopn respectively ), then -

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

The function f(x)=[(sqrt(x))/(1+x)] ; (where [ ] denotes the greatest integer function) is (A) Continuous but non-differentiable for x>0 (B) Continuous and differentiable for x>=0 (C) Discontinuous exactly at two points for x>=0 (D) Non-differentiable exactly at one point for x>0

f is continuous at x=3 but not at x=2 The function f(x)=|2sgn2x|+2 has

Let f(x)= { [(x)/(2x^(2)+|x|)", "x!=0],[1", "x=0] } then f(x) is (A) continuous but non-differentiable at x=0 (B) differentiable at x=0 (C) discontinuous at x=0 (D) none of these

If f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(3))",",1 le x le 2):} , where [.] and {.} denotes greatest integerd and fractional part of x respectively, then the number of points, which is not differentiable, is