Evaluate the following: `\ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6`

Simplify: (x+sqrt(x-1))^6+(x-sqrt(x-1))^6

Evaluate the following: (sqrt(x+1)+sqrt(x-1))^(6)+(sqrt(x+1)-sqrt(x-1))^(6)

If alpha and beta be the coefficients of x^6 and x^2 respectively in the expansion of (x+sqrt(x^2 -1))^6+(x-sqrt(x^2 -1))^6 , then

Evaluate the following: lim_(xrarr2)(x^2-4)/(sqrt(3x-2)-sqrt(6-x))

Find the number of terms in the expansion of (x+sqrt(x^(2)-1))^(6)+(x-sqrt(x^(2)-1))^(6)

Evaluate the following limit: (lim)_(x rarr1)((2x-3)(sqrt(x)-1))/(3x^(2)-3x-6)

Evaluate the following limits : lim_(x rarr 2) (sqrt(3x-2) -x)/(2-sqrt(6-x))

Evaluate the following limits: lim_(xrarr0)((sqrt(1+x^(2))-sqrt(1+x))/(sqrt(1+x^(3))-sqrt(1+x)))

Find (dy)/(dx) in the following: y=sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

Evaluate the following limits : lim_(x to infty)(sqrt(x^(2)+x+1)-sqrt(x^(2)+1)) .