時x趨近於0時 (tan x-x)/(x^2 tan x) 的極限

時x趨近於0時 (tan x-x)/(x^2 tan x) 的極限

原式=lim(x→0)(tanx-x)/x^3 (tanx~x)
=lim(x→0)(1/cos^2(x)-1)/(3x^2) (洛必達法則)
=lim(x→0)sin^2(x)/(3x^2)*lim(x→0)1/cos^2(x)
=1/3*1 (sinx~x)
=1/3