Let `f(x)=(log x)/x,` and solution of `f(x)=k` be denoted by `g (k)*` {where k < 0}.`g:(-oo, 0)->(0, 1),` then `y=g(x)` will be

Let f(x)=(log x)/(x), and solution of f(x)=k be denoted by g(k). {where k<0}g:(-oo,0)rarr(0,1), then y=g(x) will be

If f(x) and g(x) be continuous functions in [0,a] such that f(x)=f(a-x),g(x)+g(a-x)=2 and int_0^a f(x)dx=k , then int_0^a f(x)g(x)dx= (A) 0 (B) k (C) 2k (D) none of these

f(x)=(cos^(2)x)/(1+cos x+cos^(2)x) and g(x)=k tan x+(1-k)sin x-x, where k in R,g'(x)=

Let f_(k) ""=(1)/(k) ( sin ^(k) x + cos^(k)x), where x in RR and k gt 1 then f_(4) (x)- f_(6)(x) equals -

Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th) derivative of f (x) w.r.t. x, k in N. If f^(2m) (0) != 0, m belongs to N, then m =

Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th) derivative of f (x) w.r.t. x, k in N. If f^(2m) (0) != 0, m in N, then m =

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,y in R,f(x) is differentiable and f'(0)=1. Let g(x) be a derivable function at x=0 and follows the function rule g((x+y)/(k))=(g(x)+g(y))/(k), k in R,k ne 0,2 and g'(0)=lambda If the graphs of y=f(x) and y=g(x) intersect in coincident points then lambda can take values

If f(x)=kx^(2)-3x+k and g(x) = x - 1 be two polynomials, then g(x) will be a factor of f(x) when k =