f(x) = `(x^n + (pi/3)^n)/(x^(n-1) + (pi/3)^(n-1))`,(n is an even number, then which of the following is correct

For every integer n, let a_n and b_n be real numbers Let function f : R rarr R be given by f(x)={(a_n+ sin pi x, "for" x in [2n, 2n+1]), (b_n+cos pi x, "for" x in (2n-1,2n)):} for all integers n If f is continuous, then which of the following hold(s) for all n ?

Let f:(-pi/2, pi/2)->R , f(x) ={lim_(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(tanx)^(2n)) x in 0 , n in N ; 1 if x=0 which of the following holds good? (a) f(-(pi^(-))/4)=f((pi^(+))/4) (b) f(-(pi^(-))/4)=f(-(pi^(+))/4) (c) f((pi^(-))/4)=f((pi^(+))/4) (d) f(0^(+))=f(0)=f(0^(-))

If f_(n) = {{:( (f_(n-1))/(2) " when " f_n-1 "is an even number"), (3* f_(n-1) + 1 " when " f_(n-1) " is an odd number "):} and f_(1) = 3 , then f_(5) =

The function f(x)=(4sin^(2)x-1)^(n)(x^(2)-x+1),n in N has a local minimum at x=(pi)/(6). Then (a) n is any even number (b) n is an odd number ( ) n is odd prime number (d) n is any natural number

Is the function f(x)=x^(3n), n in N even?

Evaluate: lim_(x rarr oo)sin^(n)((2 pi n)/(3n+1)),n in N

The period of f(x)=sin((pi x)/(n-1))+cos((pi x)/(n)),n in Z,n>2

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number