一个微积分题
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绛旓細鏂规硶濡備笅鍥炬墍绀猴紝璇疯鐪熸煡鐪嬶紝绁濆涔犳剦蹇細
绛旓細=鈭(0.1)1/鈭(2-u²)du-蟺/4 =0
绛旓細涓涓婊℃按鐨勮姳鐡讹紝鍏剁旱鎴潰濡傚浘锛屾槸涓涓姏鐗╃嚎y=ax^2锛坅>0锛夛紝闂綋鍊炬枩瑙捨变负澶氬皯鏃讹紝姝ｅソ鍊掓帀浜嗕竴鍗婄殑姘达紵 绛旀锛氬厛绠楀嚭鐡跺瓙鐩寸珛姘存弧鏃剁殑浣撶Н鐢涓涓Н鍒灏卞彲浠ヤ簡锛岀粨鏋滅瓑浜嶸=蟺h^2/(2a); 绗簩姝ワ紝鍋囪鍊炬枩瑙掍负伪锛屾濂藉掓帀浜嗕竴鍗婄殑姘达紝閲嶆柊寤虹珛鍧愭爣绯伙紝浠ゆ鏃剁摱鐨勫绉拌酱涓簓杞达紝...
绛旓細1 lim(x鈫3锛寉鈫0)sin(xy)/tan(xy)=lim(x鈫3,y鈫0)sin(xy)'/tan(xy)'=lim(x鈫3锛寉鈫0)xcos(xy)/[x/(cos(xy))^2]=lim(x鈫3锛寉鈫0)cos(xy)=1 2 lim(x鈫0,y鈫2) (1+sin(xy))^(y/x)=lim(x鈫0,y鈫2)锛1+sin(xy))^(y/sin(xy))^(sin(xy)/x)=lim(x...
绛旓細锛堝啝绗﹀彿鐨勮鍒欐槸绗涓涓姝ｏ紝绗簩涓礋锛屼緷娆′氦鏇匡紝鏈鍚庝竴涓洿绾跨殑灏辨槸姹绉垎锛屽叾浠栫殑鐩存帴甯︾鍙风浉鍔犲氨鍙互浜嗭紝鐩存帴鍙互寰楀埌1寮忥級鎴戜妇鐨勪緥瀛愭槸鈭玴nekxdx绫诲瀷鐨勶紝pn鎸囩殑鏄椤瑰紡锛岃繖绉嶇被鍨嬮兘鏄痯n閫愰」姹傚锛宔kx閫愰」绉垎 鍏跺疄锛屽仛杩欎釜棰樼洰鍊掓病鑺卞闀挎椂闂达紝鏁板琛ㄨ揪寮忓お闅炬墦浜嗐傚儚杩欑棰樼洰锛屼綘涓轰粈涔堜笉闂悓瀛...
绛旓細娉ㄦ剰鈭珁dx鏄嚱鏁皔=f锛坸)鍦ㄥ尯闂达紙x1锛寈2)闂寸殑闈㈢Н锛岃棰樼洰璇翠簡锛屼袱鐐逛箣闂存槸鐩寸嚎锛岄偅涔堝浘褰㈡槸涓涓姊舰锛屾褰笂搴曞姞涓嬪簳=y1+y2,楂=x2-x1,闈㈢Н=锛坸2-x1)(y1+y2)/2 鎵浠ュ師寮=蠁锛坹2)e^x2-蠁锛坹1)e^x1-m(y2-y1)-m锛坸2-x1)(y1+y2)/2 =蠁锛坹2)e^x2-m/2锛坸2-x1)(y1...
绛旓細閫変慨2-2 1.6 寰Н鍒鍩烘湰瀹氱悊 涓銆侀夋嫨棰 1锛庝笅鍒楃Н鍒嗘纭殑鏄()[绛旀]銆A A.214 銆B.54 C.338 銆D.218 [绛旀]銆A [瑙ｆ瀽]銆2锛2x2锛1x4dx锛2锛2x2dx锛2锛21x4dx 锛13x32锛2锛嬶紞13x锛32锛2 锛13(x3锛峹锛3)2锛2 锛138锛18锛13锛8锛18锛214.鏁呭簲閫堿.3.1锛1|x|dx...
绛旓細f(x)鐨涓涓鍘熷嚱鏁颁负cos(2x),鍒:鈭玣(x)dx=cos(2x)+C 涓よ竟姹傚锛歠(x)=- 2sin(2x)鎵浠ワ細鈭玣'(x)dx=f(x)+C=- 2sin(2x)+C
绛旓細鈭玡^x*sinxdx =e^sinx-鈭玡^cosxdx =e^xsinx-(e^xcosx+鈭玡^xsindx)=e^x (sinx-cosx)-鈭玡^xsinxdx 鎵浠2鈭玡^xsinxdx=e^x(sinx-cosx)+C1 鈭玡^xsinxdx=e^x(sinx-cosx)/2+C 鈭2sinxdx = -2cosx + C 鈭村師寮 = e^x(sinx-cosx)/2 -2cosx + C ...
绛旓細楂榵鐨勬埅闈㈠崐寰勪负(x/7)*13 闈㈢Н=蟺(13x/7)^2 浣撶Н鍏=蟺(13x/7)^2 dx 鐒跺悗鎼埌椤堕儴鎵闇鍋氬姛 =mgh =蟻蟺(13x/7)^2 dx *(7-x)=[169蟻蟺/49]x^2(7-x) dx 鎬诲姛 =鈭玔0,3][169蟻蟺/49]x^2(7-x) dx =[169蟻蟺/49][(7/3)x^3-(1/4)x^4]|[0,3]=[169蟻蟺/...
