If `f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c)`, `v=sqrt(c)` `-sqrt(c-1),(c >1),` then (a)`fog(u) < fog(v)` (b)`gof(u) < gof(v)`(c) `gof(u) > gof(v)` (d) `fog(u) > fog(v)`

If f(x)=x+sinx ,g(x)=-(x-2)^(1/3) ,u=sqrt(2001)-sqrt(2000) , v=sqrt(2000)- sqrt(1999) then (a) fog(u) (c) gof(u) > gof(v) quad quad quad quad quad quad quad quad (d) None of these

If f is an increasing function AA x in R and u=sqrt(c+1)-sqrt(c);v=sqrt(c)-sqrt(c-1);(c>1) ,then

if int tan^(-1)sqrt(x)dx=u tan^(-1)sqrt(x)-sqrt(x)+c then u=

If f(x)=(u)/(v) then f'(x)=(1)/(v^(3))

Let u=sqrt(c+1)-sqrt(c)andv=sqrt(c)-sqrt(c-1),cgt1 and let f(x)=In (1+x),AAx in (-1,oo). Statement I f(u)gtf(v),AAcgt1 because Statement II f(x) is increasing ffunction, hence for ugtv,f(u)gtf(v).

If f(x)=(x)/(sqrt(1-x^(2))),g(x)=(x)/(sqrt(1+x^(2))) then ( fog )(x)=

If the function f(x)=(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x)) If the value of f((pi)/(3))=a+b sqrt(c) then a+b+c=

Find fog and gof , if f(x)=x+1 , g(x)=e^x

If f(x)=3x+1,g(x)=x^(2)+2 find fog(x) and gof(x)

if f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then f'(3)+f'(6)= (A) 0 (B) 1 (C) 2 (D) 1/2