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

Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

Let f(x) = (xe)^(1/|x|+1/x); x != 0, f(0) = 0 , test the continuity & differentiability at x = 0

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

Let g(x)=f(x)+f(1-x) and f''(x)<0 , when x in (0,1) . Then f(x) is

Show that the function f(x)={x^msin(1/x), x=0 ,0 ,\ \ \ x!=0 ,\ \ \ \ \ \ \x=0 is differentiable at x=0 , if m >1

If f(x)={{:(x^(p+1)cos.(1)/(x)":", x ne 0),(0":", x=0):} then at x = 0 the function f(x) is

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

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