求y=sinx的绝对值在x=0处的连续性和可导性，急求！！！ 讨论f（x）=sinx在x=0处的连续性和可导性
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y'(0+)= lim(x→0+) (sinx-sin0)/(x-0)=1。左右导数不相等。所以不可导。
lim(x→0-)|sinx|=lim(x→0+)|sinx|=|sin(0)|
∴y在x=0处连续；
∵y=sinx 0≤x≤π
y=-sinx π≤x≤0
∴y'(0-)=-cos(0)=-1
y'(0+)=cos(0)=+1
∴y在x=0处不可导。
连续可导
y'(0-)= lim(x→0-) (sinx-sin0)/(x-0)=1
y'(0+)= lim(x→0+) (sinx-sin0)/(x-0)=1=y'(0-)
y=|x|在x=0处是不可导的，不能这样用夹逼定理。
绛旓細y'(0-)= lim(x鈫0-) (|sinx|-|sin0|)/(x-0)= lim(x鈫0-) (-sinx-sin0)/(x-0)=-[sin锛坸+0锛/2*cos(x-0)/2]/(x-0)=-1銆倅'(0+)= lim(x鈫0+) (sinx-sin0)/(x-0)=1銆傚乏鍙冲鏁颁笉鐩哥瓑銆傛墍浠ヤ笉鍙銆
绛旓細y=|sinx| 鍦▁=0澶勭殑宸︽瀬闄愬拰鍙虫瀬闄愰兘绛変簬0,涓斿綋x=0鏃,y=0.璇ュ嚱鏁板湪x=0鍑虹殑宸︽瀬闄愮瓑浜庡彸鏋侀檺绛変簬鍑芥暟鍊,鍒欐鍑芥暟杩炵画y'=|sinx|'褰搙>0鏃,y'=cosx,x=0澶勭殑鍙虫瀬闄愮瓑浜1褰搙<0鏃,y'=-cosx,x=0澶勭殑宸︽瀬闄愮瓑浜-1瀵兼暟鐨勫乏鏋侀檺涓嶇瓑浜庡彸鏋侀檺 鍒欐鍑芥暟鍦╔=0澶勪笉鍙 ...
绛旓細閫氳繃瀹為檯渚嬪瓙锛屾瘮濡sinx-cosx鐨缁濆鍊煎湪0鍒跋涓婄殑绉垎鍜缁濆鍊約inx鍦ㄤ笂闄2蟺涓嬮檺0鐨勭Н鍒嗭紝鎴戜滑鍙互鐪嬪埌鍦ㄨ繖浜涙儏鍐典笅锛屽嚱鏁扮殑瀵兼暟鎬ц川涔熸敮鎸佷簡y = |sinx|鍦▁ = 0鐨勯潪鍙鎬с
绛旓細x鈫0-,y=-sinx,y'=-cosx=-1 x鈫0+,y=sinx,y'=cosx=1 鍙y=|sinx|鍦▁锛0澶勶紝宸﹀鏁颁笌鍙冲鏁板瓨鍦紝浣嗕笉鐩哥瓑锛屽洜姝や笉鍙 绗簩涓鐩,鐢变簬鍑芥暟鍦▁=1澶勪笉杩炵画锛屽綋鐒跺鏁颁笉瀛樺湪浜
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绛旓細鏈 ||sin(x)|-0|=|sin(x)|<=|x|<d=e/2<e 锛岄偅涔堝綋x鈫0鏃讹紝|sin(x)|鈫0 锛涜 |sin(0)|=0 锛屾墍浠 |sin(x)| 鍦0鐐硅繛缁紱瀵兼暟鐨勮瘽灏辨槸浣犱笂闈㈠啓鐨勶紝鐢变簬鍙冲鏁=1锛屽乏瀵兼暟=-1锛屽乏鍙冲鏁颁笉鐩哥瓑鎵浠sin(x)|鍦0鐐逛笉鍙锛岃繖閲屽垎鍒眰宸﹀彸瀵兼暟鏃跺叾瀹炵敤浜嗕竴涓瀬闄愶紝灏辨槸褰 x鈫...
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