If `f(x)=x/(sinx)a n dg(x)=x/(tanx),w h e r e0ltxlt=1,` then in this interval

Discuss monotonocity of f(x)=x/(sinx)a n d g(x)= x / (tanx), w h e r e

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

If f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)= ______ for x>2

Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integers. If f(g(20))-g(f(20))=28 , then which of the following is not true? a=15 b. a=6 c. b=14 d. b=3

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(pi)/(2) ,then g(x) is increasing in

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

Prove that the curves y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x) is differentiable function, have common tangents at common points.

If x int_0^xsin(f(t))dt=(x+2)int_0^x tsin(f(t))dt ,w h e r ex >0, then show that f^(prime)(x)cotf(x)+3/(1+x)=0.