`(x^(4)+2x^(3)+3x^(2)+4x+5)-:(x+1)`

Evaluate lim_(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) - 9x^(4) - x^(3) + 35x^(2) + 6x + 30)/(x^(5) - 2x^(4) + 4x^(2) - 9x + 6)

The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roots x _(1), x _(2), x _(3), x_(4) such that x _(1) lt x _(2) lt x _(3)lt x _(4) and product of two roots is unity, then : x _(1)x _(2) +x_(1)x_(3) + x_(2) x _(4) +x_(3) x _(4)=

check whether p(x) is a multiple of g(x) or not (i) p(x) =x^(3)-5x^(2)+4x-3,g(x) =x-2. (ii) p(x) =2x^(3)-11x^(2)-4x+5,g(x)=2x+1

Find the derivative of (x^(3) - 3x^(2) + 4)(4x^(5) + x^(2) -1) :

Evauate lim_(xto1) (x^(4)-3x^(4)+2)/(x^(3)-5x^(2)+3x+1).

Evaluate lim_(x to 0) [(3x^(2) + 4x + 5)/(x^(2) - 2x + 3)]

The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [1//2,3] is

Evaluate the following limits : Lim_(x to 1) (x^(4) - 3x^(3) +2)/(x^(3)-5x^(2)+3x+1)

Divide x^(4)+5x^(3)-x^(2)+4x-3 by x-2 and verify the division algorithm.

Simplify the following : 5x^(4) - 7x^(2) +8x - 1 +3x^(2) - 9x^(2) + 7 - 3x^(4)+11x - 2 +8x^(2)