Let `f(x),xgeq0,` be a non-negative continuous function. If `f^(prime)(x)cosxlt=f(x)sinxAAxgeq0,` then find `f((5pi)/3)`

Let f(x),x>=0, be a non-negative continuous function.If f'(x)cos x =0, then find f((5 pi)/(3))

Let f(x),xgeq0, be a non-negative continuous function, and let f(x)=int_0^xf(t)dt ,xgeq0, if for some c >0,f(x)lt=cF(x) for all xgeq0, then show that f(x)=0 for all xgeq0.

Let f(x),xgeq0, be a non-negative continuous function, and let F(x)=int_0^xf(t)dt ,xgeq0, if for some c >0,f(x)lt=cF(x) for all xgeq0, then show that f(x)=0 for all xgeq0.

Let f(x), xge0 , be a non-negative continous function,and let F(x) = int_(0)^(x)f(t)dt, xge0 , if for some cgt0,f(x)lec F(x) for all xge0 , then show that f(x)=0 for all xge0 .

Let f(x),x>=0, be a non-negative continuous function,and let F(x)=int_(0)^(x)f(t)dt,x>=0, if for some c>0,f(x) =0, then show that f(x)=0 for all x>=0.

Let f(x) be a non-negative continuous function defined on R such that f(x)+f(x+1/2)=3 , then the value of 1/1008 int_(0) ^(2015) f(x) dx is

Let f(x) be a non-negative continuous function defined on R such that f(x)+ f(x+(1)/(2))=3 ,then the value of (1)/(1008)*int_(0)^(2016)f(x)dx

Let f(x) be a non negative continuous and bounded function for all xge0 .If (cos x)f(x) lt (sin x- cosx)f(x) forall x ge 0 , then which of the following is/are correct?