If `f(x)={x, x leq 0 and -x , x gt 0 and g(x)=f(x)+|x|` then `lim_(x->0^+)(log_(|sinx|)x)^(g(x))=`

If (x)={x,x 0 and g(x)=f(x)+|x| then lim_(x rarr0^(+))(log_(|sin x|)x)^(g(x))=

If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)), then at x=0,g(x) is

If f(x)={:{(2x+1,x le 0),(3(x+1),x gt 0):} . Find lim_(x to 0) f(x) and lim_(x to 1) f(x) .

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

If f(x)=sin(sinx) an f f'(x) +tan xf'(x)+g(x)=0 , then g(x) is :

If f(x)=sgn(x)={(|x|)/(x),x!=0,0,x=0 and g(x)=f(f(x)) then at x=0,g(x) is

If f(x)=sinx, g(x)=x^2 and h(x)=log x, find h[g{f(x)}].

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to

Let f be a differentiable function satisfying f(xy)=f(x).f(y).AA x gt 0, y gt 0 and f(1+x)=1+x{1+g(x)} , where lim_(x to 0)g(x)=0 then int (f(x))/(f'(x))dx is equal to