高数（7）需要用到的公式是?
\u9ad8\u7b49\u6570\u5b66\u53ca\u5e94\u7528\uff0c\u586b\u5199\u516c\u5f0f\uff01\uff01\u8bbef(x)\uff1dx2^x\uff0d1\uff0c\u5219f(x)\u5728(\uff0d\u221e\uff0c\uff0b\u221e)\u5185\u8fde\u7eed.
\u7531\u9898\u610f\uff0c\u6240\u7528\u95ed\u533a\u95f4[a,b]\u7684\u53f3\u7aef\u70b9b\uff1d1\uff0c\u56e0\u4e3af(1)\uff1d1\uff1e0\uff0c\u6240\u4ee5\u8981\u4f7f\u7528\u96f6\u70b9\u5b9a\u7406\uff0c\u9700\u4fdd\u8bc1f(a)\uff1c0\uff0c\u6240\u4ee5\u53ef\u4ee5\u53d6a\uff1d0\uff0cf(0)\uff1d\uff0d1\uff1c0\uff08\u5f53\u7136a\u6709\u65e0\u7a77\u591a\u4e2a\u53d6\u503c\uff09
\u5728[0,1]\u4e0a\u4f7f\u7528\u96f6\u70b9\u5b9a\u7406\uff0c\u5373\u5f97\u7ed3\u8bba.
差化积及倍角公式
绛旓細鐗瑰埆娉ㄦ剰鐨勬槸x鈫掆垶鏃讹紝1 / x鏄棤绌峰皬锛屾棤绌峰皬鐨勬ц川寰楀埌鐨勬瀬闄愭槸0銆2銆佺浜屼釜閲嶈鏋侀檺鐨勫叕寮锛歭im (1+1/x) ^x = e锛坸鈫掆垶锛夊綋x鈫掆垶鏃讹紝锛1+1/x锛夛季x鐨勬瀬闄愮瓑浜巈锛涙垨褰搙鈫0鏃讹紝锛1+x锛夛季锛1/x锛夌殑鏋侀檺绛変簬e銆傚叾浠栧叕寮忥細1銆佹き鍦嗗懆闀(L)鐨勭簿纭绠瑕佺敤鍒绉垎鎴栨棤绌风骇鏁扮殑姹傚拰锛...
绛旓細浣跨敤鐨鏄 wallis 锛堢摝閲屾柉鍏紡锛锛岀洿鎺ュ鐢ㄥ叕寮忓嵆鍙紱
绛旓細涓夎鍑芥暟璇卞鍏紡 鐩綍 璇卞鍏紡鐨勬湰璐 甯哥敤鐨勮瀵煎叕寮 鍏朵粬涓夎鍑芥暟鐭ヨ瘑 1. 鍚岃涓夎鍑芥暟鐨勫熀鏈叧绯诲紡 2. 鍚岃涓夎鍑芥暟鍏崇郴鍏褰㈣蹇嗘硶 3. 涓よ鍜屽樊鍏紡 4. 浜屽嶈鐨勬寮､浣欏鸡鍜屾鍒囧叕寮 5. 鍗婅鐨勬寮､浣欏鸡鍜屾鍒囧叕寮 6. 涓囪兘鍏紡 7. 涓夊嶈鐨勬寮A...
绛旓細缃簬骞抽潰鐩磋鍧愭爣绯讳腑锛宎>0鏃跺紑鍙ｅ悜涓婏紝a<0鏃跺紑鍙ｅ悜涓(a=0鏃朵负涓鍏冧竴娆″嚱鏁)銆俢>0鏃跺嚱鏁板浘鍍忎笌y杞存鏂瑰悜鐩镐氦锛宑<0鏃跺嚱鏁板浘鍍忎笌y杞磋礋鏂瑰悜鐩镐氦锛宑=0鏃舵姏鐗╃嚎缁忚繃鍘熺偣锛宐=0鏃舵姏鐗╃嚎瀵圭О杞翠负y杞(褰撶劧a=0涓攂鈮0鏃惰鍑芥暟涓轰竴娆″嚱鏁)銆2銆侀《鐐鍏紡y=a(x+h)*2+k锛(h锛宬)=(-b/(2a)锛(...
绛旓細鏈珷鏄珮鑰冨懡棰樼殑涓讳綋鍐呭涔嬩竴,搴斿垏瀹炶繘琛屽叏闈佹繁鍏ュ湴澶嶄範,骞跺湪姝ゅ熀纭涓,绐佸嚭瑙ｅ喅涓嬭堪鍑犱釜闂:(1)绛夊樊銆佺瓑姣旀暟鍒楃殑璇佹槑椤荤敤瀹氫箟璇佹槑,鍊煎緱娉ㄦ剰鐨勬槸,鑻ョ粰鍑轰竴涓暟鍒楃殑鍓 椤瑰拰 ,鍒欏叾閫氶」涓 鑻 婊¤冻 鍒欓氶」鍏紡鍙啓鎴 .(2)鏁板垪璁＄畻鏄湰绔犵殑涓績鍐呭,鍒╃敤绛夊樊鏁板垪鍜岀瓑姣旀暟鍒楃殑閫氶」鍏紡銆佸墠 椤瑰拰鍏紡鍙婂叾鎬ц川...
绛旓細楂樻暟娉板嫆鍏紡棰橈細姝ら鍙敤鑾卞竷灏艰尐鍏紡鍋氾紝璇︾粏杩囩▼瑙佸浘銆傝繖閬撻珮鏁伴锛屾槸涓や釜鍑芥暟涔樼Н鐨勯珮闃跺鏁伴棶棰樸傚叾涓紝褰搉澶т簬2鏃讹紝x²鐨刵闃跺鏁颁负0锛屾墍浠ワ紝鍙互鐢ㄥ叧浜庝箻绉殑楂橀樁瀵兼暟鍏紡锛屽嵆鑾卞竷灏艰尐鍏紡锛屽彲寰椼
绛旓細鍥句竴鏄瑙ｃ傚浘浜屾槸鎴戞晠鎰忓啓鐨勯敊瑙ｏ紝绗簩椤瑰拰绗笁椤癸紝鍙兘璇存槑n>3锛岃繕鏄緱涓嶅埌姝ｇ‘缁撴灉銆
绛旓細瀹氫箟鍩 x 鈭 (-1, 1).浠 t = arccosx锛 鍒 t 鈭 (0, 蟺), x = cost锛 dx = -sintdt 鈭玜rccosxdx/鈭歔(1-x^2)^3] = 鈭玹(-sintdt)/(sint)^3 = 鈭-tdt/(sint)^2 = 鈭玹dcott = tcott - 鈭玞ottdt = tcott - ln|sint| + C = xarccosx/鈭(1-x^2) - ln...
绛旓細鍏舵锛楂樻暟鐨鍏ㄧО鏄楂樼瓑鏁板锛屼竴鑸ぇ瀛︽暟瀛﹀垎涓哄洓闂ㄨ绋嬶細楂樼瓑鏁板涓婂唽銆楂樼瓑 鏁板涓嬪唽銆佺嚎鎬ф暟瀛︺佹鐜囪涓庢暟鐞嗙粺璁★紝閭ｄ箞楂樻暟涓涔熷氨鏄寚楂樼瓑鏁板涓婂唽銆傚畠鍖呮嫭鍑芥暟涓庢瀬闄愩佸鏁颁笌寰垎銆佸井鍒嗕腑鍊煎畾鐞嗕笌瀵兼暟鐨勫簲鐢ㄣ佷笉瀹氱Н 鍒嗐佸畾绉垎銆佸畾绉垎鐨勫簲鐢ㄣ佺┖闂磋В鏋愬嚑浣曚笌鍚戦噺浠ｆ暟涓冪珷鍐呭銆傝岄珮鏁颁簩涓昏鑰冧袱涓...
绛旓細瀵瑰姬闀跨殑鏇茬嚎绉垎鐨勫仛娉曟槸鍖栦负瀹氱Н鍒嗭紝鍏抽敭鏄姬寰垎ds鐨勫寲绠銆傚綋鏇茬嚎鐨勬柟绋嬫槸鏋佸潗鏍噐=r(胃)鏃讹紝ds=鈭歔r^2+(r')^2]d胃锛岀Н鍒嗏埆f(x,y)ds=鈭玣(r(胃)cos胃,r(胃)sin胃)鈭歔r^2+(r')^2]d胃銆
