The value of `p ( x ) = ( x − 1 ) ( x + 1 )` for `p ( 1 )` is :

If absolute maximum value of f(x)=(1)/(|x-4|+1)+(1)/(|x+8|+1)is(p)/(q), (p,q are coprime) the (p-q) is……… .

Find the values of p and q , so that f(x)={{:(x^(2)+3x+p, ifxle1),(qx+2,ifx gt1):} is differentiable at x = 1

The value of lim_(x to 1) ((p)/(1-x^(p))-(q)/(1-xq)),p,q,inN, equals

The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2) + 2 (4p^(2) - 1) x + 4(2p^(2)+1) for real values of p and x is

The value of lim_(x to1)(p/(1-x^p)-q/(1-x^q)),p ,q , in N , equal (a) (p+q)/2 (b) (p q)/2 (c) (p-q)/2 (d) sqrt(p/q)

Let P(x) be a polynomial of degree 11 such that P(x) = (1)/(x + 1) for x = 0, 1, 2, 3,"…."11 . The value of P(12) is.

P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p(x) has maxima at x = -1 and p(x) has minima at x=1 then The value of P(2) is (a) -15 (b) -16 (c) -17 (d) -22 (c) -17 (d) -22

The value int^(2)_(-2) {p" In"((1+x)/(1-x))+q" In "((1-x)/(1+x))-2+r}dx depends on the value of

Let P(x) be quadratic polynomical with real coefficient such tht for all real x(1) the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then If the range of P(x) is [m, oo) then 'm' is less then

Find the value of p for which the quadratic equation (p+1)x^2+ -6(p+1)x+3 (p +9)=0, p != -1 has equal roots. Hence, find the roots of the equation.