`underset(x→0)lim(1+x)^(1/x)`

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: (a) underset(x to 0)lim (arc cos (1-x))/sqrtx (b) underset(x to pi//4)lim (ln tan x)/(1-cot x) (c ) underset(x to 0) lim(1)/(sin x) ln (1+a sin x)

Find the limits: (a) underset(x to 0)lim (1-cos x)/(x^2) (b) underset(x to 0)lim (tanx-sinx)/(x^(3)) (c ) underset(x to 1)lim ""(cos (pix//2))/(1-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 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))=