lim x趋近于0时 tanx-x比x的三次方 tanx-x⼀x^3

2024-12-29 14:41:30
推荐回答(1个)
回答1:

(1)tanx泰勒展开tanx=x+x^3/3+o(x^5)则lim(x→0) (tanx-x)/x^3=1/3(2) 0/0罗必塔lim(x→0) (tanx-x)/x^3 罗必塔=lim(x→0) sin^2x/3x^2*cos^2x=lim(x→0) 1/3*(sinx/x)^2*(1/cosx)^2=1/3