`underset(x→∞)lim[1+1/x]^(x)`

Find underset(x to oo)lim (1+1/x^2)^x

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))=

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

The limit underset(x to 2)lim (2^(x)+2^(3-x)-6)/(sqrt2^(-x)-2^(1-x)) is equal to

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")