limcosx/x怎么求x→∞ lim x→∞ cosx/x. 等于多少？
\u6c42lim cosx/x \uff08x\u8d8b\u5411\u221e\uff09\u5f53x\u8d8b\u5411\u65e0\u7a77\u65f6\uff0c\uff082x-cosx)/x=2-cosx/x\u3002\u5176\u4e2dcosx\u6c38\u8fdc\u5728-1\u548c1\u4e4b\u95f4\uff0c\u800cx\u662f\u65e0\u7a77\u5927\uff0c\u6240\u4ee5cosx/x\u8d8b\u8fd1\u4e8e0\uff0c\u6240\u4ee5\uff082x-cosx)/x\u8d8b\u8fd1\u4e8e2\uff0c\u4e5f\u5c31\u662f
lim(x\u8d8b\u5411\u65e0\u7a77\uff09
\uff082x-cosx)/x=2
\u89e3\uff1a\u56e0\u4e3alim
1/x
\uff08x\u8d8b\u5411\u221e\uff09=0
|cosx|\u22641
\u6240\u4ee5\u6839\u636e\u65e0\u7a77\u5c0f\u548c\u6709\u754c\u51fd\u6570\u4e58\u79ef\u662f\u65e0\u7a77\u5c0f\uff0c
\u5f97
\u539f\u5f0f=0
夹逼准则，
0=lim-1/x≤limcosx/x≤lim1/x=0
cosx是有界值，故得0
因为x→∞,分母为∞，cosx小于等于1，cosx的最大值为1，就可以理解成∞的倒数，即为无穷小0
绛旓細涔熷彲浠ワ紝cosx鏄繛缁嚱鏁帮紝鎵浠ワ紝lim(x鈫0)cosx=cos0=1 銆愯繛缁у瀹屼簡浠ュ悗鍙互鐩存帴搴旂敤銆
绛旓細=limcosx锛坸/sinx锛夛紝x瓒嬩簬0鏃=limcosx=1
绛旓細濡傛槸棰樼洰鏄繖鏍风殑 (cosx)^(1/sinx)璁緔= (cosx)^(1/sinx)lny=ln(cosx)/sinx limx->0 ln(cosx)/sinx=limx->0 -sinx/cosx/cosx=0 娲涘繀杈炬硶鍒 鎵浠 鍘熸瀬闄=limx->0 e^lny=e^0=1 濡傛槸棰樼洰鏄繖鏍风殑 cos(x^(1/sinx))limx->0 cos(x^(1/sinx))=cos[limx->0 x^(1/sinx)...
绛旓細cosx鏄 鍛ㄦ湡鍑芥暟 锛屽尯闂存槸[-1,1]锛屽墠鑰呭湪x鈫掆垶鏃跺彉鎴恖imxcosx鍙湅鍑 鏃犵┓澶 涔樹互涓涓尟鑽＄殑缁撴灉锛屽叾缁撴灉鏄 鍑芥暟 鏇茬嚎 鍦ㄦ棤绌峰ぇ鍜屾棤绌峰皬涔嬮棿鎸崱鍙樺寲锛屼笉瀛樺湪瓒嬭繎浜庢棤绌峰皬杩樻槸鏃犵┓澶э紱鍚庤呭湪x鈫0鏃讹紝cosx绛変簬1锛limcosx/x鍙涓烘槸 甯告暟 1闄や互涓涓秼鍚戜簬0鐨勬暟锛岀粨鏋滃氨鏄棤绌峰ぇ銆
绛旓細鈶=lim2sin2x/3sin3x/=4/9锛屸懙=limcosx=cosa锛屸懚=lime^锛坙n锛1+3x锛/sinx锛=lime^锛堬紙3/锛1+3x锛夛級/cosx锛=e^3
绛旓細瑙ｏ細娉ㄦ剰鍒0/0鍨嬬敤娲涘繀杈炬硶鍒欙紝绛変环鏃犵┓灏弜->0,sinx~x,limcosx=1浜庢槸鍘熷紡=x->0lim(cosx/sinx)(x-sinx)/(xsinx)=x->0lim(1/sinx)(x-sinx)/(xsinx)=x->0lim(x-sinx)/(xsinx^2)=x->0lim(x-sinx)/(x^3)=x->0lim(1-cosx)/(3x^2)=x->0limsinx/(6x)=x->0limx/(...
绛旓細杩欎釜瑕佺敤澶归煎噯鍒欏晩 0<=1-cosx=2sin²x/2<=2*(x/2)²=x²/2 鍥犱负 lim0=lim(x->0)x²/2=0 鎵浠 鐢卞す閫煎噯鍒欙紝寰 褰搙瓒嬭繎浜0鏃秎im1-cosx=0 鍗 褰搙瓒嬭繎浜0鏃limcosx=1
绛旓細楂樹腑瑙ｆ硶锛屽鍑芥暟f锛坸锛=cosX杩涜姹傚鍑芥暟杩愮畻涓篻锛坸锛=-sinX 浠锛坸锛=0锛岃В寰梮=0鏃跺師鍑芥暟f锛坸锛夊彇寰楀畠鐨勬瀬闄 f锛0锛=1锛屽畬鎴
绛旓細x鈫掆垶 鍒欏垎瀛cosx鍦╗-1,1]闇囪崱,鍗虫湁鐣 鍒嗘瘝涓 e^x鈫+鈭 e^-x鈫0 鎵浠ュ垎姣嶈秼浜庢棤绌 鎵浠ュ師寮=0
绛旓細lim cosx/x=0 |cosx|鈮1涓烘湁鐣屽嚱鏁帮紝x涓烘棤绌峰ぇ閲 x鈫掆垶
