f(x)=sin2x,求在点x=0处的极限 设函数f(x)={sin 2x,x<0;k,x=0;xsin...
f\uff08x\uff09=x sin\uff081\uff0fx\uff09\u5728\u70b9 \u5904x=0\u7684\u6781\u9650lim xsin(1/x)=0
x->0
\u65e0\u7a77\u5c0f\u4e58\u6709\u754c\u51fd\u6570\u4ecd\u4e3a\u65e0\u7a77\u5c0f
f(x)={sin 2x,x0}f(x)\u5728x=0\u5904\u5de6\u6781\u9650\u662f0\uff0c\u53f3\u6781\u9650\u662f3\uff0c\u6240\u4ee5\u4e0d\u7ba1\u53d6k\u7b49\u4e8e\u591a\u5c11\u90fd\u4e0d\u80fd\u4f7f\u5de6\u6781\u9650\u7b49\u4e8e\u53f3\u6781\u9650\u3002\u6240\u4ee5\u8fd9\u6837\u4ebak\u503c\u4e0d\u5b58\u5728\u3002
lim<x→0>sin2x=0
绛旓細杩欓亾棰樼浜岄棶灏辨槸闂綘|f(x)-g(x)|鐨勬渶澶у 绗竴闂細|f(45)-g(45)|=|sin(90)-cos(90+30)|=1.5 绗簩闂細璁F(x)=|sin2x-cos(2x+30)|=|鈭氾浚3sin(2x-30)| 鍒欐渶澶у间负鈭氾浚3
绛旓細杩欐槸澶嶅悎鍑芥暟 u=2x锛u'=2 鍒檡=f(x)=sinu 鎵浠'(x)=cosu*u'=2cos2x 鎵浠'(0)=2*cos0=2
绛旓細f'x 2cos2x f'(fx )=2cos2sin2x 鍙︽敞鎰(ffx)' =2cos2sin2x* 2cos2x
绛旓細f(x) = sin2x = sinu, 鍏朵腑 u = 2x f'(x) = cosu路(u)' = cos2x (2x)' = 2cos2x
绛旓細sinxcosx=1/2sin2x 鎵浠f(x)=1/2(sin2x-cos2x)+1/2=1/2*鈭2*sin(2x-45掳)+1/2 鎵浠(x)鍊煎煙鏄痆-1/2*鈭2+1/2,1/2*鈭2+1/2]f(a)=1/2*鈭2*sin(2x-45掳)+1/2=5/6 鎵浠in(2x-45掳)=鈭2/3 sin2a=sin(2a-45掳+45掳)=sin(2x-45掳)cos(45掳)+cos(2x-45...
绛旓細[]鏄彇鏁村嚱鏁扮殑绗﹀彿锛孾x-1]琛ㄧず鐨勬槸涓嶅ぇ浜巟-1鐨勬渶澶ф暣鏁般倄鈫0+锛孾x-1]鈫-1锛泋鈫0-锛孾x-1]鈫-2
绛旓細sin2x鏄痜(x)鐨勪竴涓師鍑芥暟 鎵浠 鈭玣(x)dx=sin2x+C 瀹氱Н鍒嗗氨鏄氨姹傚師鍑芥暟鐨勯泦鍚,鈭玣(x)dx浠ｈ〃鐨勬剰鎬濇槸,姹俧(x)杩欎釜鍑芥暟鐨勫師鍑芥暟鐨勯泦鍚.sin2x鏄痜(x)鐨勪竴涓師鍑芥暟,鎶妔in2x鍔犱笂浠绘剰甯告暟C,閮芥槸f(x)鐨勫師鍑芥暟
绛旓細y=sin2x鐨勫鏁版槸2cos2x銆傛嫇灞曠煡璇嗭細1銆佸鏁帮紙Derivative锛夛紝涔熷彨瀵煎嚱鏁板笺傚張鍚嶅井鍟嗭紝鏄井绉垎涓殑閲嶈鍩虹姒傚康銆傚綋鍑芥暟y=f锛坸锛鐨勮嚜鍙橀噺x鍦ㄤ竴鐐箈0涓婁骇鐢熶竴涓閲徫攛鏃讹紝鍑芥暟杈撳嚭鍊肩殑澧為噺螖y涓庤嚜鍙橀噺澧為噺螖x鐨勬瘮鍊煎湪螖x瓒嬩簬0鏃剁殑鏋侀檺a濡傛灉瀛樺湪锛宎鍗充负鍦▁0澶勭殑瀵兼暟锛岃浣渇鈥欙紙x0锛夋垨df锛坸0...
绛旓細瑙ｇ瓟锛氾紙1锛夊懆鏈熷嚱鏁扮殑瀹氫箟鏄痜(x+T)=f(x)鈭 姹傚懆鏈熸椂锛岄渶瑕佸彉鎴愯繖绉嶅舰寮忥紝鍗 sin(2x+2蟺锛=sin2x 寰楀埌锛歴in{2(x+蟺锛夛綕=sin2x 鈭 鍛ㄦ湡鏄 锛2锛墆=Asin(wx)鐨勫懆鏈熸槸T=2蟺/|w| 鏈涓瓀=2 鈭 鍛ㄦ湡鏄疶=2蟺/2=蟺
绛旓細澶嶅悎鍑芥暟锛屼竴瀹氳涓ゆ姹傚銆傦紙1锛夊厛瀵sin2x鏁翠綋姹傚锛屼负=cos2x锛2锛夊啀瀵2x姹傚涔熷氨鏄妸绗竴娆＄殑瀵间箻浠2锛岋紙3锛夊嵆鏈鍚庣粨鏋滀负2cos2x
