8£®ÒÑÖªµãPΪÍÖÔ²$\frac{{x}^{2}}{16}$+$\frac{{y}^{2}}{12}$=1Éϵ͝µã£¬EFΪԲN£ºx2+£¨y-1£©2=1µÄÈÎÒ»Ö±¾¶£¬Çó$\overrightarrow{PE}•\overrightarrow{PF}$×î´óÖµºÍ×îСֵÊÇ£¨¡¡¡¡£©
A£®16£¬12-4$\sqrt{3}$B£®17£¬13-4$\sqrt{3}$C£®19£¬12-4$\sqrt{3}$D£®20£¬13-4$\sqrt{3}$

·ÖÎö ¸ù¾ÝÌâÒ⣬µÃ|NE|=|NF|=1ÇÒ$\overrightarrow{NF}=-\overrightarrow{NE}$£¬ÓÉ´Ë»¯¼òµÃ$\overrightarrow{PE}•\overrightarrow{PF}$=$|\overrightarrow{PN}{|}^{2}$-1£¬¸ù¾ÝÍÖÔ²·½³ÌÓëÁ½µãµÄ¾àÀ빫ʽ£¬Çó³öµ±PµÄ×Ý×ø±êΪ-3ʱ£¬$|\overrightarrow{PN}{|}^{2}$È¡µÃ×î´óÖµ20£¬Óɴ˼´µÃ$\overrightarrow{PE}•\overrightarrow{PF}$=$|\overrightarrow{PN}{|}^{2}$-1µÄ×î´óÖµ£¬µ±PµÄ×Ý×ø±êΪ$2\sqrt{3}$ʱ£¬$|\overrightarrow{PN}{|}^{2}$È¡µÃ×îСֵ$13-4\sqrt{3}$£¬Óɴ˼´µÃ$\overrightarrow{PE}•\overrightarrow{PF}$=$|\overrightarrow{PN}{|}^{2}$-1µÄ×îСֵ£®

½â´ð ½â£º¡ßEFΪԲNµÄÖ±¾¶£¬¡à|NE|=|NF|=1£¬ÇÒ$\overrightarrow{NF}=-\overrightarrow{NE}$£¬
Ôò$\overrightarrow{PE}•\overrightarrow{PF}$=£¨$\overrightarrow{PN}$+$\overrightarrow{NE}$£©•£¨$\overrightarrow{PN}$+$\overrightarrow{NF}$£©
=£¨$\overrightarrow{PN}$+$\overrightarrow{NE}$£©•£¨$\overrightarrow{PN}$$-\overrightarrow{NE}$ £©
=${\overrightarrow{PN}}^{2}-{\overrightarrow{NE}}^{2}$=$|\overrightarrow{PN}{|}^{2}$-1£¬
ÉèP£¨x0£¬y0£©£¬ÔòÓÐ$\frac{{{x}_{0}}^{2}}{16}+\frac{{{y}_{0}}^{2}}{12}=1$¼´x02=16-$\frac{4}{3}$y02
ÓÖN£¨0£¬1£©£¬¡à$|\overrightarrow{PN}{|}^{2}$=${{x}_{0}}^{2}+£¨{y}_{0}-1£©^{2}=-\frac{1}{3}£¨{y}_{0}+3£©^{2}+20$£¬
¶øy0¡Ê[-2$\sqrt{3}$£¬2$\sqrt{3}$]£¬
¡àµ±y0=-3ʱ£¬$|\overrightarrow{PN}{|}^{2}$È¡µÃ×î´óÖµ20£¬Ôò$\overrightarrow{PE}•\overrightarrow{PF}$=$|\overrightarrow{PN}{|}^{2}$-1=20-1=19£¬
µ±y0=$2\sqrt{3}$ʱ£¬$|\overrightarrow{PN}{|}^{2}$È¡µÃ×îСֵ$13-4\sqrt{3}$£¬Ôò$\overrightarrow{PE}•\overrightarrow{PF}$=$|\overrightarrow{PN}{|}^{2}$-1=$13-4\sqrt{3}$-1=$12-4\sqrt{3}$£®
¡à$\overrightarrow{PE}•\overrightarrow{PF}$×î´óÖµºÍ×îСֵÊÇ£º19£¬$12-4\sqrt{3}$£®
¹ÊÑ¡£ºC£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ¼òµ¥ÐÔÖÊ£¬¿¼²éÁËÏòÁ¿ÖªÊ¶ÒÔ¼°Åä·½·¨µÄÔËÓã¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®ÒÑÖªÊýÁÐ{an}µÄǰnÏîºÍSnÂú×ã2Sn=3an-3£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Éèbn=2an-3n£¬ÇóÊýÁÐ{bn}µÄnÏîºÍTn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÓÃÇØ¾ÅÉØËã·¨¼ÆËã¶àÏîʽf£¨x£©=12+35x-8x2+6x4+5x5+3x6ÔÚX=-4ʱµÄֵʱ£¬V3µÄֵΪ£¨¡¡¡¡£©
A£®-144B£®-136C£®-57D£®34

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®¸´ÊýzÂú×ãzi-z=4+2iµÄ¸´ÊýzΪ£¨¡¡¡¡£©
A£®3-iB£®1+3iC£®3+iD£®-1-3i

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®ÒÑÖªÏòÁ¿$\vec m=£¨2cosx£¬-\sqrt{3}sinx£©£¬\vec n=£¨cosx£¬\;2cosx£©$£¬É躯Êý$f£¨x£©=\vec m•\vec n£¬\;x¡ÊR$£®
£¨¢ñ£©Çóº¯Êýf£¨x£©µÄ×îСÕýÖÜÆÚºÍµ¥µ÷µÝ¼õÇø¼ä£»
£¨¢ò£©Èô·½³Ìf£¨x£©-k=0ÔÚÇø¼ä$[0£¬\frac{¦Ð}{2}]$ÉÏÓÐʵÊý¸ù£¬ÇókµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®Éèf£¨x£©ÊÇ£¨-¡Þ£¬+¡Þ£©Éϵļõº¯Êý£¬Ôò²»µÈʽf£¨2£©£¼f£¨2x+1£©µÄ½â¼¯ÊÇ£¨¡¡¡¡£©
A£®$£¨0£¬\frac{1}{2}£©$B£®$£¨-¡Þ£¬\frac{1}{2}£©$C£®$£¨\frac{1}{2}£¬+¡Þ£©$D£®$£¨-¡Þ£¬0£©¡È£¨\frac{1}{2}£¬+¡Þ£©$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®ÒÑÖªa=${£¨\frac{2}{5}£©^{\frac{2}{5}}}$£¬b=${£¨\frac{3}{5}£©^{\frac{2}{5}}}$£¬c=${log_{\frac{3}{5}}}\frac{2}{5}$£¬Ôòa¡¢b¡¢c´óС¹ØÏµÊÇ£¨¡¡¡¡£©
A£®a£¼c£¼bB£®b£¼a£¼cC£®c£¼a£¼bD£®a£¼b£¼c

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®ÉèÊýÁÐ{an}µÄǰnÏîºÍΪSn£¬ÒÑÖªa1=1£¬Sn+1=2Sn+n+1£¨n¡ÊN*£©
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Èôbn=$\frac{{a}_{n}+1}{{a}_{n}•{a}_{n+1}}$£¬ÇóÊýÁÐ{bn}µÄǰnÏîºÍTn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

20£®Ñ§Ï°À׷澫Éñǰ°ëÄêÄÚijµ¥Î»²ÍÌüµÄ¹Ì¶¨²ÍÒξ­³£ÓÐË𻵣¬Ñ§Ï°À׷澫ÉñʱȫÐ޺㻵¥Î»¶ÔѧϰÀ׷澫Éñǰºó¸÷°ëÄêÄÚ²ÍÒεÄËð»µÇé¿ö×÷ÁËÒ»¸ö´óÖÂͳ¼Æ£¬¾ßÌåÊý¾ÝÈç±í£º
Ë𻵲ÍÒÎÊýδË𻵲ÍÒÎÊý×Ü ¼Æ
ѧϰÀ׷澫Éñǰ50150200
ѧϰÀ׷澫Éñºó30170200
×Ü  ¼Æ80320400
ÔòÓÐ97.5%ÒÔÉϵİÑÎÕÈÏΪËð»Ù²ÍÒÎÊýÁ¿ÓëѧϰÀ׷澫ÉñÓйأ¿
²Î¿¼Êý¾Ý£º
P£¨K2¡Ýk0£©0.050.0250.0100.0050.001
k03.8415.0246.6357.87910.828

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸