求极限，1的无穷型怎么做？ 高等数学求极限，1的无穷大次方型，看不懂第一种方法，求解！
1\u7684\u65e0\u7a77\u578b\u6781\u9650\u600e\u4e48\u6c42\u8fd9\u4e5f\u662f\u672a\u5b9a\u578b\u7684\u6781\u9650
\u901a\u5e38\u4f7f\u7528\u5bf9\u6570\u8f6c\u6362
\u5373\u5f97\u5230a^b=e^[lna /(1/b)]
\u4e8e\u662f\u6307\u6570\u4e3a0/0\u578b
\u8ba1\u7b97\u6781\u9650\u540e\u518d\u53d6e\u6307\u6570\u5373\u53ef
\u540c\u5b66\uff0c\u8fd9\u662f\u7528\u7684\uff081+0\uff09^\u221e=e
\u6ce8\u610f\u8fd9\u91cc\u76840\u548c\u221e\u4e92\u4e3a\u5012\u6570\u3002
\u539f\u5f0f\u62ec\u53f7\u91cc\u8fb9\u63d0\u51fa\u4e00\u4e2a2^(1/x),\u4e5f\u5c31\u662f\u5916\u8fb9\u76f4\u63a5\u63d0\u51fa\u4e00\u4e2a2
\u90a3\u4e48\u91cc\u9762\u5c31\u53d8\u6210\u4e86\u89e3\u6cd5\u4e2d\u62ec\u53f7\u5185\u5c0f\u62ec\u53f7\u5185\u5bb9
\u53f3\u4e0a\u89d2\u7684\u5f62\u5f0f\u5c31\u662f\u9020\u90a3\u4e2a\u201c0\u201d\u90e8\u5206\u7684\u5012\u6570
\u518d\u770b\u770b\u591a\u4e86\u4ec0\u4e48\uff0c\u53bb\u6389\u5b83\uff0c\u4e5f\u5c31\u662f\u4e2d\u62ec\u53f7\u5916\u7684\u6307\u6570\u90e8\u5206
\u6700\u540e\u51fa\u6765e
\u5728\u505a\u5c31\u884c\u4e86\u3002
绛旓細1鐨勨垶娆℃柟鍨嬫眰鏋侀檺鐨勬柟娉曞涓嬶細1銆佸埄鐢ㄩ噸瑕佹瀬闄愶細lim锛坸鈫0锛夛紙1+x锛塣锛1/x锛=e锛岃繖涓噸瑕佹瀬闄愬湪姹1鐨勨垶娆℃柟鍨嬬殑鏋侀檺鏃堕潪甯告湁鐢銆傞氳繃灏嗚〃杈惧紡杩涜鍙樺舰锛屼娇寰楀叾鍙互涓庤繖涓噸瑕佹瀬闄愮殑褰㈠紡鐩稿尮閰嶏紝浠庤屽緱鍑烘瀬闄愬笺2銆佽浆鍖栦负鎸囨暟鍑芥暟锛氬皢1鐨勨垶娆℃柟鍨嬬殑鏋侀檺杞寲涓烘寚鏁板嚱鏁扮殑鏋侀檺銆傝繖绉嶆柟娉曢渶瑕佷娇鐢ㄦ寚鏁...
绛旓細涓鐨勬棤绌峰瀷姹傛瀬闄愬叕寮忓涓嬶細1鐨勬棤绌锋鏋侀檺鍒╃敤e^lim[g(x)lnf(x)] 涓巈^a銆俛=limf(x)g(x)杞寲鍚庯紝鍙厛鍖栫畝锛屽啀鍒╃敤娲涘繀杈炬硶鍒欐垨鑰呯瓑浠锋棤绌峰皬绛夋潵姹傛瀬闄愩1鐨勬棤绌锋鏂规槸鏋侀檺鏈畾寮忕殑涓绉嶏紝鏈畾寮忔槸鎸囧鏋滃綋x鈫抶0(鎴栬厁鈫掆垶)鏃讹紝涓や釜鍑芥暟f(x)涓巊(x)閮借秼浜庨浂鎴栬呰秼浜庢棤绌峰ぇ锛岄偅涔堟瀬闄恖i...
绛旓細涓鐨勬棤绌峰瀷鏄寚褰撲竴涓嚱鏁板湪鑷彉閲忚秼浜庢棤绌峰ぇ鏃讹紝涓庝竴涓棤绌峰ぇ鍚岄樁浣嗘瘮瀹冧綆闃剁殑鍑芥暟鐨勬瀬闄愩傚浜涓鐨勬棤绌峰瀷锛鎴戜滑鍙互浣跨敤浠ヤ笅姹傛瀬闄鍏紡锛歭im(x->鈭) (a^x / x^b) = +鈭, 褰揳>1鎴朾<0鏃讹紱lim(x->鈭) (logₐ(x) / x^b) = 0, 褰揳>1鎴朾>0鏃躲傚叾涓紝a鏄竴涓甯告暟锛...
绛旓細1鐨勬棤绌娆℃柟鍨嬫瀬闄愭眰瑙濡備笅锛1銆侀渶瑕佷簡瑙ｄ竴浜涘熀鏈殑鏋侀檺姒傚康銆傚綋n瓒嬪悜浜庢棤绌峰ぇ鏃锛1^n鐨勬瀬闄愮瓑浜1銆傝繖鏄洜涓烘棤璁簄鍙樺緱澶氬ぇ锛1^n鐨勭粨鏋滄绘槸1銆傚悓鏍峰湴锛0^n鐨勬瀬闄愪篃绛変簬0锛屽洜涓烘棤璁簄鍙樺緱澶氬ぇ锛0^n鐨勭粨鏋滄绘槸0銆2銆佽冭檻涓绉嶇壒娈婄殑鏋侀檺鎯呭喌锛屽嵆褰搙瓒嬪悜浜0鏃讹紝锛1+x锛塣鈭炵殑鏋侀檺銆傛垜浠彲浠ラ噰鐢ㄦ寚...
绛旓細灏辨槸杩欐牱璁＄畻宀鏉ョ殑锛佸笇鏈涘浣犳湁甯姪銆
绛旓細1鈭炲瀷鏈畾寮忓叕寮璁＄畻鏂规硶濡備笅锛1鈭炲瀷鏈畾寮忓叕寮忥細銖憏锛漧im(x鈫掆垶){銖慬1+(a/x)]}/锛1/x锛夛紝鏈畾寮忔槸鎸囧鏋滃綋x鈫抶0(鎴栬厁鈫掆垶)鏃讹紝涓や釜鍑芥暟f(x)涓巊(x)閮借秼浜庨浂鎴栬呰秼浜鏃犵┓澶э紝閭ｄ箞鏋侀檺lim[f(x)/g(x)](x鈫抶0鎴栬厁鈫掆垶)鍙兘瀛樺湪锛屼篃鍙兘涓嶅瓨鍦紝閫氬父鎶婅繖绉嶆瀬闄愮О涓烘湭瀹氬紡锛...
绛旓細姹傛瀬闄鐨勬椂鍊 1鐨勬棤绌澶ф鏂规樉鐒朵篃鏄湭瀹氬瀷 涓嶈兘纭畾鍏舵瀬闄愬肩殑澶у皬 閭ｄ箞灏辫杩涜杞崲 鍗1^鈭=e^(ln1 *鈭)姝ゆ椂鍐嶆妸ln1 *鈭炶浆鎹负 0/0 鍐嶄娇鐢ㄦ礇蹇呰揪娉曞垯锛屾潵姹傛瀬闄愬煎嵆鍙
绛旓細y=tanx^tan2x lny=tan2xlntanx=lntanx/cot2x 0/0鍨嬶紝鐢ㄦ礇蹇呰揪娉曞垯 limlny 涓婁笅姹傚 =lim(1/tanx*sec^2x)/(-2csc^2 2x)=lim-cosx/sinx*1/cos^2x*2sin^2 2x =lim-1/sinxcosx*2sin^2 2x =-lim2/sin2x*2sin^2 2x =-limsin 2x =-sin蟺/2 =-1 鎵浠ュ師寮=1/e ...
绛旓細1鐨勬棤绌娆℃柟鍙互鎹㈡垚浠涓哄簳鐨勬寚鏁板嚱鏁板啀杩涜璁＄畻鎴栬呭埄鐢ㄧ浜屼釜閲嶈鏋侀檺杩涜璁＄畻銆1鐨勬棤绌峰ぇ娆℃柟鍏紡浠嬬粛銆1鐨勬棤绌锋鏋侀檺鍒╃敤e^lim涓巈^a,a=limf(x)g(x)杞寲鍚庯紝鍙厛鍖栫畝锛屽啀鍒╃敤娲涘繀杈炬硶鍒欐垨鑰呯瓑浠锋棤绌峰皬绛夋潵姹傛瀬闄锛1鐨勬棤绌锋鏂规槸鏋侀檺鏈畾寮忕殑涓绉嶏紝鏈畾寮忔槸鎸囧銆俵im(n->鈭烇級锛撅紙n^2/...
绛旓細1鐨勬棤绌娆℃瀬闄愬埄鐢╡^lim[g(x)lnf(x)] 涓巈^a锛宎=limf(x)g(x)杞寲鍚庯紝鍙厛鍖栫畝锛屽啀鍒╃敤娲涘繀杈炬硶鍒欐垨鑰呯瓑浠锋棤绌峰皬绛夋潵姹傛瀬闄銆1鐨勬棤绌锋鏂规槸鏋侀檺鏈畾寮忕殑涓绉嶏紝鏈畾寮忔槸鎸囧鏋滃綋x鈫抶0(鎴栬厁鈫掆垶)鏃讹紝涓や釜鍑芥暟f(x)涓巊(x)閮借秼浜庨浂鎴栬呰秼浜庢棤绌峰ぇ锛岄偅涔堟瀬闄恖im [f(x)/g(x)] (x鈫...
