`underset(x→∞)lim ((x+1)^(2/3)-(x-1)^(2/3))`

Find the limits : (a) underset(x to oo)lim ((2x^(2)+3)/(2x^(2)+5))^(8x^(2)+3) (b) underset(x to 0)lim ((1+tan x)/(1+tan x))^(1//sin x) (c ) underset(x to 1)lim (1+sin pi x)^(cot pi x) (d) underset(x to a)lim ((sin x)/(sin a))^(1//(x-a)) (a ne kpi," with k integer")

Find the limits : underset(x to oo)lim ((1+x)/(2+x))^((1-sqrtx)//(1-x)) (b) underset(x to oo)lim ((x^(2)+2x-1)/(2x^(2)-3x-2))^((2x+1)//(x-1))

The value of the limit underset(x to oo)lim ((x^(2)-1)/(x^(2)+1))^(x^(2)) equal to

If underset(x to 1)lim (ax^(2)+bx+c)/((x-1)^(2))=2" then "underset(x to 1)lim ((x-a)(x-b)(x-c))/((x+1))=

Evaluate : underset(x to 1)(lim) ((x+x^(2) + x^(3) +……….+x^(n)) -n)/(x-1)

underset(x to a)(Lim) ((a+2x)^((1)/(3)) - (3x)^((1)/(3)))/((3a+x)^((1)/(3)) - (4x)^((1)/(3))) (a ne 0) is equal to :