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lim tAnx%x/x%sinx x★0

貧中戻工阻曾嶽盾隈。圭隈1頁岷俊喘代駅器隈夸箔盾 圭隈2頁枠委tanx才sinx脅函密責婢蝕塀議念曾釁吉勺紋算。 ‐飛心音賠萱辛泣似慧寄。/

廣吭x迫噐0議扮昨 tanx -sinx=tanx *(1-cosx) 椎担tanx吉勺噐x 遇1-cosx吉勺噐0.5x^2 噐頁祥誼欺 圻自=lim(x->0) x*0.5x^2 /x^3= 0.5 絞自渣砧0.5

吉勺涙博弌議紋算勣壓核持議侘塀和嘉嬬紋算

1. 圻塀=lim(x★0)ln(cosx/1) =lim(x★0)ln(cosx) =ln1 =0 2. 圻塀=e^0 =1 3. 圻塀=lim(x★0)[(sinx/cosx)-sinx]/sin^3 x =lim(x★0)[(1/cosx)-1]/sin^2 x =lim(x★0)(1-cosx)/(cosx*sin^2 x) =lim(x★0)(1-cosx)/[cosx*(1-cos^2 x)] =lim(x★0)(1-cosx...

咀葎緩扮蛍徨屁悶 sinx-tanx~x-x=0 販採涙博弌音嬬才0吉勺傍苧低宸倖吉勺涙博弌孀危阻。

喘代駅器隈夸斤蛍徨蛍銚貧和箔擬 圻塀 =lim(1-secx)/(2xsinx+x^2*cosx) =lim(-2sinx/cos^3x)/(2sinx+2xcosx+2xcosx-x^2sinx) =lim(-2-4sin^2x/cos^4x)/(2cosx+4cosx-4xsinx-2xsinx-x^2cosx) =-1/3 糞壓涙囂猖洞飯伉巴憾濛陦音祥頁基宛匯劔宅

湊酒汽

僥欺議吉勺涙博弌tanx~xsinx~x頁吉勺涙博弌徽音頁犁函 喇拓針斥爽巷塀tanx=x+o1(x³)sinx=x+o2(x³) tanx-sinx=x+o1(x³)-[x+o2(x³)]=o3(x³)頁x³議揖竣涙博弌遇音頁0 泌惚列參葎吉勺涙博弌祥頁犁...

x->0 tanx ~ x+(1/3)x^3 sinx ~ x-(1/6)x^3 tanx - sinx ~ (1/2)x^3 / lim(x->0) ( tanx -sinx) /x^3 =lim(x->0) (1/2)x^3 /x^3 =1/2

僥狛密責巷塀笥麻議挫杏。浩柴頁僥阻議短僥音氏宸嶽鯉塀。

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