Let `f: [0,pi/2rarr[0,1]` be a differentiable function such that `f(0) = 0, f (pi/2)=1,` then

Let f:[0,(pi)/(2)rarr[0,1] be a differentiable function such that f(0)=0,f((pi)/(2))=1 then

Let f:R rarr R be a differentiable function such that f(0)=0,f(((pi)/(2)))=3 and f'(0)=1 If g(x)=int_(x)^((pi)/(2))[f'(t)cos ect-cot t cos ectf(t)]dt for x in(0,(pi)/(2)] then lim_(x rarr0)g(x)=

Let f:[0.8]rarr R be differentiable function such that f(0)=0,f(4)=1,f(8)=1 then which of the following hoid (s) good?

Let f:R rarr R be a differentiable function such that f(0),f((pi)/(2))=3 and f'(0)=1. If g(x)=int_(x)^((pi)/(2))[f'(t)csc t-cot t csc tf(t)]dt for x in(0,(pi)/(2)] then lim_(x rarr0)g(x)=

Let f:R rarr R be a twice differential function such that f((pi)/(4))=0,f((5 pi)/(4))=0 and f(3)=4 then show that there exist a c in(0,2 pi) such that f'(c)+sin c-cos c<0

Let f:R rarr[0,oo) be a differentiable function so that f'(x) is continuous function then int((f(x)-f'(x))e^(x))/((e^(x)+f(x))^(2))dx is equal to

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

Let f:(0, oo)rarr(0, oo) be a differentiable function such that f(1)=e and lim_(trarrx)(t^(2)f^(2)(x)-x^(2)f^(2)(t))/(t-x)=0 . If f(x)=1 , then x is equal to :

Let f:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .