let `f(x) = { g(x).cos(1/x) if x!= 0 and 0 if x= 0` , where g(x) is an even function differentiable at x= 0 passing through the origin then f'(0)

Let f(x)=sin x,g(x)={{max f(t),0 pi Then number of point in (0,oo) where f(x) is not differentiable is

A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

If f(x)={sin x,x<0 and cos x-|x-1|,x<=0 then g(x)=f(|x|) is non-differentiable for

Let f(x)=|x-1|+|x-2| and g(x)={min{f(t):0<=t<=x,0<=x<=3 and x-2,x then g(x) is not differentiable at

Let g(x)=1+x-[x] and f(x)=-1 if x 0, then f|g(x)]=1x>0

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

Let f(x)=cot^-1g(x)] where g(x) is an increasing function on the interval (0,pi) Then f(x) is

Let f(x) b a function for all x in R and f(0)=1. Then g(x)=f(x)-sqrt((1-cos2x)/2) at x=0 a) is differentiable at x=0 and its value is 1 b) is differentiable at x=0 and its value is 0 c) is non differentiable at x=0 and its graph has a sharp turn at x =0 d) is non differentiabe at x =0 and its graph has vertical tangent at x =0

Let f ( x) = int _ 0 ^ x g (t) dt , where g is a non - zero even function . If f(x + 5 ) = g (x) , then int _ 0 ^ x f (t ) dt equals :