2£®É躯Êýf£¨x£©=lnx-$\frac{1}{2}a{x^2}$-bx£®
£¨1£©µ±a=-2£¬b=3ʱ£¬Çóº¯Êýf£¨x£©µÄ¼«Öµ£»
£¨2£©ÁîF£¨x£©=f£¨x£©+$\frac{1}{2}a{x^2}+bx+\frac{a}{x}£¨{0£¼x¡Ü3}£©$£¬ÆäͼÏóÉÏÈÎÒâÒ»µãP£¨x0£¬y0£©´¦ÇÐÏßµÄбÂÊk¡Ü$\frac{1}{2}$ºã³ÉÁ¢£¬ÇóʵÊýaµÄÈ¡Öµ·¶Î§£»
£¨3£©µ±a=0£¬b=-1ʱ£¬·½³Ìf£¨x£©=mxÔÚÇø¼ä[1£¬e2]ÄÚÇ¡ÓÐÁ½¸öʵÊý½â£¬ÇóʵÊýmµÄÈ¡Öµ·¶Î§£®

·ÖÎö £¨1£©½«a£¬bµÄÖµ´øÈëf£¨x£©£¬Çó³öº¯Êýf£¨x£©µÄµ¼Êý£¬½â¹ØÓÚµ¼º¯ÊýµÄ·½³Ì£¬Çó³öº¯ÊýµÄ¼«Öµ¼´¿É£»
£¨2£©Çó³öF£¨x£©µÄµ¼Êý£¬ÎÊÌâת»¯Îªa¡Ý${£¨-\frac{1}{2}x_0^2+{x_0}£©_{min}}$£¬´Ó¶øÇó³öaµÄ·¶Î§¼´¿É£»
£¨3£©Çó³öf£¨x£©µÄ½âÎöʽ£¬ÎÊÌâת»¯Îªm=1+$\frac{lnx}{x}$ÔÚÇø¼ä[1£¬e2]ÄÚÇ¡ÓÐÁ½¸öʵÊý½â£®

½â´ð ½â£º£¨1£©ÒÀÌâÒ⣬f£¨x£©µÄ¶¨ÒåÓòΪ£¨0£¬+¡Þ£©£¬
µ±a=-2£¬b=3ʱ£¬f£¨x£©=lnx+x2-3x£¬£¨x£¾0£©£¬
f¡ä£¨x£©=$\frac{£¨2x-1£©£¨x-1£©}{x}=0£¬µÃx=\frac{1}{2}$»òx=1
Áбíf£¨x£©µÄ¼«´óֵΪ$f£¨\frac{1}{2}£©=-ln2-\frac{5}{4}$£¬
f£¨x£©µÄ¼«Ð¡ÖµÎªf£¨1£©=-2£»
£¨2£©F£¨x£©=lnx+$\frac{a}{x}$£¬x¡Ê£¨0£¬3]£¬
ÔòÓÐk=F'£¨x0£©=$\frac{{{x_0}-a}}{{{x_0}^2}}¡Ü\frac{1}{2}$£¬ÔÚ£¨0£¬3]ÉÏÓн⣬
¡àa¡Ý${£¨-\frac{1}{2}x_0^2+{x_0}£©_{min}}$
ËùÒÔ µ±x=1ʱ£¬-$\frac{1}{2}x_0^2+{x_0}$È¡µÃ×îСֵ$\frac{1}{2}$£¬¡àa¡Ý$\frac{1}{2}$£®
£¨3£©µ±a=0£¬b=-1ʱ£¬f£¨x£©=lnx+x=mx£¬£¨x¡Ê[1£¬e2]£©£¬
µÃm=1+$\frac{lnx}{x}ÔÚ[{1£¬{e^2}}]ÓÐÁ½¸öʵÊý½â$£¬
$m¡Ê[\frac{2}{e^2}+1£¬\frac{1}{e}+1£©$ʱ·½³ÌÓÐÁ½¸öʵÊý½â£®

µãÆÀ ±¾Ì⿼²éÁ˺¯ÊýµÄµ¥µ÷ÐÔ¡¢×îÖµÎÊÌ⣬¿¼²éµ¼ÊýµÄÓ¦ÓÃÒÔ¼°º¯Êýºã³ÉÁ¢ÎÊÌ⣬ÊÇÒ»µÀÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

19£®ÒÑÖªÍÖÔ²$\frac{x^2}{4}+\frac{y^2}{3}=1$£¬¶¯Ö±ÏßlÓëÍÖÔ²½»ÓÚB£¬CÁ½µã£¨BÔÚµÚÒ»ÏóÏÞ£©£®
£¨1£©ÈôµãBµÄ×ø±êΪ£¨1£¬$\frac{3}{2}$£©£¬Çó¡÷OBCÃæ»ýµÄ×î´óÖµ£»
£¨2£©ÉèB£¨x1£¬y1£©£¬C£¨x2£¬y2£©£¬ÇÒ3y1+y2=0£¬Ç󵱡÷OBCÃæ»ý×î´óʱ£¬Ö±ÏßlµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®ÒÑÖªº¯Êýf£¨x£©=$\left\{\begin{array}{l}ax+b£¬x£¼0\\{2^x}£¬x¡Ý0\end{array}\right.$£¬ÇÒf£¨-2£©=3£¬f£¨-1£©=f£¨1£©£®
£¨¢ñ£©Çóf£¨x£©µÄ½âÎöʽ£¬²¢Çóf£¨f£¨-2£©£©µÄÖµ£»
£¨¢ò£©ÇëÔÚ¸ø¶¨µÄÖ±½Ç×ø±êϵÄÚ£¬ÀûÓá°Ãèµã·¨¡±»­³öy=f£¨x£©µÄ´óÖÂͼÏó£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

10£®ÒÑÖªlnx+1¡Üx£¨x£¾0£©£¬Ôò$\frac{{{x^2}-1nx+x}}{x}£¨x£¾0£©$µÄ×îСֵΪ1£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®Èçͼ£¬ÔÚ¡÷ABCÖУ¬µãOÊÇBCµÄÖе㣬¹ýµãOµÄÖ±Ïß·Ö±ð½»Ö±ÏßAB¡¢ACÓÚ²»Í¬µÄÁ½µãM¡¢N£¬Èô$\overrightarrow{AM}=m\overrightarrow{AB}$£¬$\overrightarrow{AN}=n\overrightarrow{AC}£¨{mn£¾0}£©$£¬Ôòm+nµÄÈ¡Öµ·¶Î§Îª[2£¬+¡Þ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

7£®ÒÑÖªÍÖÔ²¦££º$\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1£¨a£¾b£¾0£©µÄ×󶥵ãΪA£¬ÓÒ½¹µãΪF2£¬¹ýµãF2×÷´¹Ö±ÓÚxÖáµÄÖ±Ïß½»¸ÃÍÖÔ²ÓÚM¡¢NÁ½µã£¬Ö±ÏßAMµÄбÂÊΪ$\frac{1}{2}$£®
£¨1£©ÇóÍÖÔ²¦£µÄÀëÐÄÂÊ£»
£¨2£©Èô¡÷AMNµÄÍâ½ÓÔ²ÔÚµãM´¦µÄÇÐÏßÓëÍÖÔ²½»ÓÚÁíÒ»µãD£¬¡÷F2MDµÄÃæ»ýΪ$\frac{6}{7}$£¬ÇóÍÖÔ²¦£µÄ±ê×¼·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

14£®²»µÈʽ22x-1£¼2µÄ½â¼¯ÊÇ£¨¡¡¡¡£©
A£®{x|x£¼0}B£®{x|x£¾1}C£®{x|x£¼2}D£®{x|x£¼1}

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®ÊýÁÐ{an}Âú×ãa1=2£¬${a_{n+1}}=\frac{{1+{a_n}}}{{1-{a_n}}}£¨n¡Ê{N^*}£©$£¬Ôòa6=-3£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®Èçͼ£¬ÔÚƽÐÐÁùÃæÌåABCD-A1B1C1D1ÖУ¬M£¬N·Ö±ðÔÚÃæ¶Ô½ÇÏßAC£¬A1CÉÏÇÒCM=2MA£¬A1N=2ND£®¼ÇÏòÁ¿$\overrightarrow{AB}=\overrightarrow a£¬\overrightarrow{AD}=\overrightarrow b£¬\overrightarrow{A{A_1}}=\overrightarrow c$£¬ÓÃ$\overrightarrow a£¬\overrightarrow b£¬\overrightarrow c$±íʾ$\overrightarrow{MN}$£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸