lim_(10^(+))root(3)(6)*alpha

Evaluate lim_(x rarr1)(root(1 3)(x)-root(7)(x))/(root(5)(x)-root(3)(x))

lim_(x rarr0)(root(3)(1+x)-root(3)(1-x))/(x)

lim_(x rarr2)(x-2)/(root(3)(x)-root(3)(2))

Let alpha (a) beta (a) be the roots of the equations : (root(3)(1+a) -1)x^(2) + (sqrt(1 + a) - 1)x + (root(6)(1 + a) - 1) = 0 , where a gt - 1 . Then lim_(a rarr 0^(+)) alpha (a) and lim_(a rarr 0^(+)) beta(a) are :

Let alpha(p) and beta(p) be the roots of the equation (root(6)(1+p)-1)x^(2)+(root(3)(1+p)+1)x+(root(9)(1+p)-1)=0 where p>-1 then lim_(p rarr0^(+))[alpha(p)+beta(p)] is equal to

let alpha(a) and beta(a) be the roots of the equation ((1+a)^((1)/(3))-1)x^(2)+((1+a)^((1)/(2))-1)x+((1+a)^((1)/(6))-1)=0 where a>-1 then,lim_(a rarr0^(+))alpha(a) and lim_(a rarr0^(+))beta(a)

Evaluate : lim_(xrarra)(root(3)(x)-root(3)(a))/(x-a)

If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = 0 , then lim_(n to oo) Sigma^(n) alpha^(r) + lim_(n to oo) Sigma^(n) beta^(r) is equal to :