Let `f(x)=xsinpix ,x > 0.` Then for all natural numbers `n ,f^(prime)(x)` vanishes at a unique point in the interval `(n , n+1/2)` a unique point in the interval `(n+1/2, n+1)` a unique point in the interval `(n , n+1)` two points in the interval `(n , n+1)`

Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) vanishes at (A)a unique point in the interval (n , n+1/2) (B)a unique point in the interval (n+1/2, n+1) (C)a unique point in the interval (n , n+1) (D)two points in the interval (n , n+1)

Let f(x)=xsinpix ,\ x >0 . Then for all natural numbers n ,\ f^(prime)(x) vanishes at (a) A unique point in the interval (n ,\ n+1/2) (b) a unique point in the interval (n+1/2,\ n+1) (c) a unique point in the interval (n ,\ n+1) (d) two points in the interval (n ,\ n+1)

the intersection of all the intervals having the form [1+(1)/(n),6-(2)/(n)], where n is a postive integer is

Find the point of inflection of the function: f(x)=sin x (a) 0 (b) n pi,n in Z (c) (2n+1)(pi)/(2),n in Z (d) None of these

Let f(n) = [1/2 + n/100] where [x] denote the integral part of x. Then the value of sum_(n=1)^100 f(n) is

Let A = {0, 1} and the set of all natural numbers.Then the mapping f: N rarr A defined by f(2n-1) = 0, f(2n) = 1, AA n in N, is

Find the number of integers lying in the interval (0,4) where the function f(x)=(lim)_(n->oo)(cos( pix/2))^(2n) is discontinuous

Statement -1 for all natural numbers n , 2.7^(n)+3.5^(n)-5 is divisible by 24. Statement -2 if f(x) is divisible by x, then f(x+1)-f(x) is divisible by x+1,forall x in N .

If f(x) = sgn(sin^2x-sinx-1) has exactly four points of discontinuity for x in (0, npi), n in N , then

Let f(x) =x^(n+1)+ax^n, "where " a gt 0 . Then, x=0 is point of