设f(x)=x,x<=0,f(x)=x^2,x>0,当x趋于0时,则lim f(x)是
\u8bbelim\uff08X\u8d8b\u5411\u4e8e0\uff09 f(2X) / X\u7b49\u4e8e2/3 \u5219lim\uff08X\u8d8b\u54110\uff09 X/ f(3X)\u7b49\u4e8e\uff1flimf(2x)/x=2/3
\u6240\u4ee5limf(2x)/2x=1/3 \u7b49\u4ef7\u4e8elimf(3x)/3x=1/3
limf(3x)/x=1
limx/f(3x)=1
\u9996\u5148sin6x~6x\u5e76\u6ca1\u9519,\u4f46\u662f(sin6x+xf(x))~(6x+xf(x)),
"~"\u8fd9\u4e2a\u7b26\u53f7\u53ea\u5bf9\u6574\u4e2a\u5206\u5b50\u548c\u5206\u6bcd\u6709\u6548,\u800c\u90e8\u5206\u5206\u5b50\u6216\u90e8\u5206\u5206\u6bcd\u7528\u7684\u65f6\u5019\u53ef\u80fd\u4f1a\u51fa\u73b0\u9519\u8bef,
\u8fd9\u9898\u5e94\u8be5\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u4e0a\u4e0b\u6c42\u5bfc
lim f(x)=0
绛旓細鍥犱负f锛坸锛=|x| 褰搙鈮0鏃讹紝f锛坸锛=-x锛屽乏瀵兼暟涓-1 褰搙鈮0鏃讹紝f锛坸锛=x锛鍙冲鏁颁负1 宸﹀彸瀵兼暟涓嶇浉绛夛紝鎵浠ヤ笉鍙銆傚鏋滀竴涓嚱鏁板湪x0澶勫彲瀵硷紝閭ｄ箞瀹冧竴瀹氬湪x0澶勬槸杩炵画鍑芥暟銆傚嚱鏁板彲瀵煎畾涔夛細锛1锛璁緁(x)鍦▁0鍙婂叾闄勮繎鏈夊畾涔,鍒欏綋a瓒嬪悜浜0鏃,鑻 [f(x0+a)-f(x0)]/a鐨勬瀬闄愬瓨鍦, 鍒...
绛旓細璁緁(x)=x/(x²+1),姹俧(1/x)瑙ｆ瀽寮 瑙ｏ細浠1/x=u锛屽垯f(x)=x/(x²+1)=(1/x)/[1+(1/x)²]锛屾晠f(u)=u/(1+u²)锛屽嵆f(1/x)=(1/x)/[1+(1/x)²].
绛旓細y'=e^(-x)-xe^(-x)=(1-x)e^(-x)鎵浠鍦▁<1涓哄鍑芥暟,鍦▁>1涓哄噺鍑芥暟 鎵浠ュ湪x=1澶勫彇寰楁瀬澶у=f(1)=1/e y''=-e^(-x)-e^(-x)+xe^(-x)=(x-2)e^(-x)鎵浠>2涓哄嚬鍖洪棿,鍦▁<2涓哄嚫鍖洪棿 x=2鏄嫄鐐
绛旓細绛旀鏄疉 鏈夌晫鍑芥暟銆傘愯В鏋愩戞牴鎹甗x]鐨勫畾涔夛紝-1锛渇(x)鈮0 鎵浠锛宖(x)鏄湁鐣屽嚱鏁般傚彟澶栵紝f(1.4)=1-1.4=-0.4 f(-1.4)=-2-(-1.4)=-0.6 鎵浠ワ紝f(x)鏃笉鏄鍑芥暟锛屼篃涓嶆槸鍋跺嚱鏁般
绛旓細銆愮瓟妗堛戯細f'(x)=(xsinx)'=(x)'sinx+x(sinx)'=sinx+xcosx.
绛旓細f1(x) = [x]锛屼粬鐨勫彇鍊煎尯闂翠负[n,n+1) 锛屽湪杩欎釜鍖洪棿鍐呴兘鍙栦竴涓硷紝n涓烘暣鏁帮紝n鈭圼0,99]锛屽叡100涓紝鍙﹀褰搙=100鏄崟鐙殑鍙栧硷紝鍥犳鍏辨湁101涓彇鍊煎厓绱狅紱鍙栧煎厓绱犱负{0,1,2,3,4,5,6,...98,99,100} f2(x) = [2x]锛屼粬鐨勫彇鍊煎尯闂翠负[n,n+0.5) 鍜孾n+0.5,n+1)锛屽湪杩欎袱涓釜...
绛旓細绛旓細0<x<1锛宖(x)=x^2 1<x<2锛宖(x)=x 0<x<=1鏃讹細F(x)=(0鈫抶)鈭 f(t)dt =(0鈫抶)鈭玹^2 dt =(0鈫抶)(1/3)t^3 =(x^3)/3 1<=x<2鏃讹細F(x)=(0鈫抶)鈭玣(t)dt =(0鈫1)鈭玣(t)dt+(1鈫抶)鈭玣(t)dt =1/3+(1鈫抶)鈭玹dt =1/3+(1鈫抶)(1/2)t^2 =...
绛旓細璁緁(x)=x+鈭(0,x)f(u)du ,f(x)鏄彲寰嚱鏁,姹俧(x) 鎴戞潵绛 棣栭〉 鐢ㄦ埛 璁よ瘉鐢ㄦ埛 瑙嗛浣滆 甯府鍥 璁よ瘉鍥㈤槦 鍚堜紮浜 浼佷笟 濯掍綋 鏀垮簻 鍏朵粬缁勭粐 鍟嗗煄 娉曞緥 鎵嬫満绛旈 鎴戠殑 璁緁(x)=x+鈭(0,x)f(u)du ,f(x)鏄彲寰嚱鏁,姹俧(x) 鎴戞潵绛 ...
绛旓細閫塂锛岀敾鍑鸿崏鍥撅紝鐒跺悗鍒嗙被璁ㄨ鍗冲彲 璇︽儏濡傚浘鎵绀猴紝鏈変换浣曠枒鎯戯紝娆㈣繋杩介棶
绛旓細5 f(y)=(0.5y^-0.5) (fx(y^0.5)+fx(-y^0.5))= (0.5y^-0.5)(e^(y^0.5)+e^(-y^0.5))浠绘剰鐨勯殢鏈哄彉閲x锛y=x^2鐨勫垎甯冮兘鏄(0.5y^-0.5)(fx(y^0.5)+fx(-y^0.5))涓嬫鐩存帴濂楄繖涓叕寮忓氨濂斤紝涓婇潰鐨勮瘉鏄庡浜庝竴鍒囬殢鏈哄彉閲弜閮介傜敤銆
