cos(5x^(2)+8)+(1)/(root(3)(4x^(2)-1))

lim_(x rarr oo) (sqrt(x^(2) + 1) - root(3)(x^(3) + 1))/(root(4)(x^(4) + 1) - root(5) (x^(4) + 1)) equals :

underset(x to oo)lim (sqrt(x^(2)+1)-root3(x^(2)+1))/(root4(x^(4)+1)-root5(x^(4)+1)))=

Evaluate the following limits : Lim_(x to oo) (sqrt(x^(2)+1)-root3(x^(3)-1))/(root4(x^(4)+1)-root5(x^(4)+1))

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

Let the equation x^(5) + x^(3) + x^(2) + 2 = 0 has roots x_(1), x_(2), x_(3), x_(4) and x_(5), then find the value of (x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).

Test the following functions for continuity (1 ) (2x^(5) - 8x^(2) + 11)/(x^(4) + 4x^(2) + 8x^(2) + 8x+4) (2) f(x) = (3 sin^(3)x + cos^(2)x+1)/(4cosx-2)

Given y=(5x)/(root(3)((1-x)^(2)))+cos^(2)(2x+1),quad find (dy)/(dx)

If introot(3)(x).root(5)(1+root(3)(x^(4)))dx=5/8(1+x^(4/a))^((2a)/b)+c (where c is constant of integration), then value of (a+b) is

"If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)(1+8x)), then y'(0) is equal to -