A differentiable function satisfies equa...

A differentiable function satisfies equation `f(x)=int_0^x(f(t)cos(t)-cos(t-x))dt` then
(A) `f''(pi/2)=e`
(B) `lim_(x->-oo) f(x)=1`
(C) `f(x)` has minimum value `1-e^(-1)`
(D) `f'(0)=-1`

Similar Questions

Explore conceptually related problems

If a differentiable function f(x) satisfies f(x)=int_(0)^(x)(f(t)cos t-cos(t-x))dt then value of (1)/(e)(f''((pi)/(2))) is

A Function f(x) satisfies the relation f(x)=e^x+int_0^1e^xf(t)dtdot Then (a) f(0) 0

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

A Function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt* Then (a)f(0) 0

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .