If f(x) is continuous in [0,2] and f(0)=f(2). Then the equation f(x)=f(x+1) has

If f(x) is continuous on [0,2] , differentiable in (0,2) ,f(0)=2, f(2)=8 and f'(x) le 3 for all x in (0,2) , then find the value of f(1) .

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3

Let f(x)=ln(2+x)-(2x+2)/x Statement-1: The equation f(x)=0 has a unique solution in the domain of f(x) . Statement-2: If f(x) is continuous in [a , b] and is strictly monotonic in (a , b) then f has a unique root in (a , b)