sinΨ(x)=1-x²,Ψ(x)=arcsin(1-x²)为什么？怎么来的 已知f（x）＝sinx，f［Ψ（x）］＝1-x²，...
sin\u03a8(x)=1-x²\u7b49\u4e8e\u03a8(x)=arcsin(1-x²)?\u4e0d\u8be5\u662f\u03a8(x)=sin(1-x²)\u53cd\u51fd\u6570\u8fd9\u70b9\u5e38\u8bc6\u90fd\u4e0d\u4f1a\u5417\uff1f
sin\u03a8(x)=1-x²\u548c\u03a8(x)=sin(1-x²)\uff0c\u4e8c\u8005\u7b49\u4ef7\u5417\uff1f
\u5047\u5982\u662farcsin\u03a8(x)=1-x²\uff0c\u90a3\u4e48\u03a8(x)=sin(1-x²)\u5012\u662f\u6709\u53ef\u80fd\u3002\u56e0\u4e3aarcsin(sinx)=x
\u4f9b\u53c2\u8003\u3002
则ψ(x)=arcsin(1-x²)；-1≦1-x²≦1，-2≦-x²≦0，即0≦x²≦2，-√2≦x≦√2。
绛旓細sin蟺x=sin(蟺-蟺x)x瓒嬩簬1鏃,蟺-蟺x瓒嬩簬闆,鍥犳x瓒嬩簬1鏃,sin(蟺-蟺x)绛変环浜幭-蟺x.
绛旓細鐜板湪锛屾垜浠渶瑕佽冭檻鏄惁瀛樺湪姝ｆ暟 N锛屽綋 x > N 鏃讹紝f(x) > 0銆傝繖灏嗕緷璧栦簬 f(x) 鍦ㄦ鏁存暟 x 涓婄殑鍏蜂綋娉㈠姩鎯呭喌銆傝冭檻浠ヤ笅鎯呭喌锛氬鏋 x 鏄鏁帮紝f(x) = sin(x) - 1/x锛宻in(x) 鐨勫煎湪 [0, 1] 涔嬮棿锛岃 1/x 鍦 x 澧炲ぇ鏃堕愭笎瓒嬭繎浜 0銆傚洜姝わ紝瀵逛簬瓒冲澶х殑濂囨暟 x锛宖(x) 鍙兘...
绛旓細鍥炵瓟锛歽=sin²(1-x)=sin²(x-1) y'=2sin(x-1)*cos(x-1)
绛旓細鍗曡皟鍑忓皯涔熸槸瑕佹帹瀵煎嚭鏉ョ殑銆備护f(x)=x-sinx x鍙栦换鎰忓疄鏁帮紝琛ㄨ揪寮忔亽鏈夋剰涔夛紝鍑芥暟瀹氫箟鍩熶负R f'(x)=1-cosx -1鈮osx鈮1锛1-cosx鈮0锛宖'(x)鈮0锛宖(x)鑷冲鏈変竴涓浂鐐广俧(0)=0-sin0=0 鍑芥暟f(x)鏈夊敮涓闆剁偣x=0 鏂圭▼sinx=x鏈変笖鍙湁鍞竴瀹炴暟瑙=0 ...
绛旓細璇烽噰绾
绛旓細楂樹腑鐨勮瘽锛sinx锛弜 = sin(x-0)/(x-0) = limx->0 sin(x-0)/(x-0)鏍规嵁瀵兼暟鐨勫畾涔 杩欏氨鏄痵inx 鍦▁=0澶勭殑瀵兼暟 sin'x = cos x 鎵浠ュ綋x瓒嬪悜浜0锛宻inx锛弜=1 鏋侀檺鎬濇兂鐨勬濈淮鍔熻兘 鏋侀檺鎬濇兂鍦ㄧ幇浠ｆ暟瀛︿箖鑷崇墿鐞嗗绛夊绉戜腑锛屾湁鐫骞挎硾鐨勫簲鐢紝杩欐槸鐢卞畠鏈韩鍥烘湁鐨勬濈淮鍔熻兘鎵鍐冲畾鐨勩傛瀬闄愭濇兂...
绛旓細杩欎釜瑕佸垎涓嶅悓鍖洪棿鐒跺悗鐢ㄥ鍚堝嚱鏁版潵璁ㄨ
绛旓細鍥犱负姝ｅ鸡鍑芥暟sinX鐨勫彇鍊艰寖鍥存槸[-1锛1]鎵浠in²X鍙栧兼槸[0锛1]鎵浠1-sin²X鐨勫煎煙鏄痆0锛1]娉ㄦ剰鍖呮嫭0鍜1
绛旓細涓夎鍑芥暟 sin(x)/(1+x)锛1.浠x=ax+1,鍒欏畠鐨勫鏁颁负a锛屽湪浠u=lnu鍒欏畠鐨勫鏁颁负1/u鎵浠ュ浜巐n(ax+1)鍊掓暟涓簎x鐨勫掓暟涔樹互yu鐨勫鏁板嵆a/ax+1銆2.锛1-x)/(1+x锛夎繖鏄晢鐨勫鏁帮紝姣旇緝绠鍗曪紝锛1-x)/(1+x锛夌殑瀵兼暟涓-锛1+x锛-(1-x)/(1+x锛塣2=-2/(1+x锛塣2鎵浠ワ紝f(x)=銖(...
绛旓細dy 锛濓經1/锛sin锛1锛峹锛夛冀锝漝锛籹in锛1锛峹锛夛冀锛濓經1/锛籹in锛1锛峹锛夛冀锝漜os锛1锛峹锛塪锛1锛峹锛夛紳锛籧os锛坸锛1锛/sin锛坸锛1锛夛冀dx锛漜ot锛坸锛1锛塪x銆
