`lim_underset(x→+∞)``ln` `(2/x^2)`

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

Value of the underset(x to -2)lim (tan pi x)/(x+2)+underset(x to oo)lim (1+1/x^(2))^(x) is

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")

Evaluate: lim_underset(x rarr 0) (sqrt(1+x+x^(2)+x^(3))-1)/(x) .

underset(x to oo)lim (cos""2/x)^(x^2)=