时不力兮骓不逝
幼苗
共回答了20个问题采纳率:85% 举报
tanx = sinx/cosx
=(x-x^3/6+x^5/120+o(x^5))/(1-[x^2/2-x^4/24+o(x^4)])
=(x-x^3/6+x^5/120+o(x^5))*{(1+ [x^2/2+x^4/24+o(x^4)]+[x^2/2+x^4/24+o(x^4)]^2+o(x^4)}
=(x-x^3/6+x^5/120+o(x^5))*{(1+ [x^2/2+x^4/24+o(x^4)]+x^4/4+o(x^4))}
=(x-x^3/6+x^5/120+o(x^5))*{(1+ x^2/2+7x^4/24+o(x^4)}
= x + x^3/3 + 2/15*x^5 + o(x^5)
① tanx = x + o(x^2)
② tanx = x + x^3/3 + o(x^4)
③ tanx = x + x^3/3 + 2/15*x^5 + o(x^6) (∵奇函数)
1年前
6