Problem 9 - Entrance Test

lim(x→0) (sin(x^2))/(x tan x) = lim(x→0) (sin(x^2)/x^2) * (x/tan x) = lim(x→0) (sin(x^2)/x^2) * (x/tan x) = 1 * lim(x→0) (x/tan x) = lim(x→0) x/(sin x / cos x) = lim(x→0) (x/sin x) * cos x = 1 * 1 = 1.