Q. For every integer n, let an and bn be real numbers. Let function `f:R->R` be given by a `f(x)={a_n+sin pix, for x in [2n,2n+1]`, `bb_n+cos pix, for x in (2n+1,2n)` for all integers n.

Q.For every integer n,let an and bn be real numbers.Let function f:R rarr R be given by a f(x)={a_(n)+sin pi x,f or x in[2n,2n+1]-n+cos pi x,f or x in(2n+1,2n) for all integers n.

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

Let f : N rarr N be defined as f(x) = 2x for all x in N , then f is

For every integer n, int_(n)^(n+1)f(x)dx=n^(2) , then the value of int_(0)^(5)f(x)dx=

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is:

Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n in R then f (x) is: