7£®ÒÑÖªÏòÁ¿$\overrightarrow{m}$=£¨2cosx£¬1£©£¬$\overrightarrow{n}$=£¨sinx£¬2cos2x£©£¬Áîf£¨x£©=$\overrightarrow{m}•\overrightarrow{n}$£®
£¨1£©Çóº¯Êýf£¨x£©µÄµ¥µ÷µÝÔöÇø¼ä£»
£¨2£©½«º¯Êýy=f£¨x£©Í¼ÏóÏòÓÒÆ½ÒÆ$\frac{¦Ð}{4}$¸öµ¥Î»ºó£¬µÃµ½º¯Êýy=g£¨x£©µÄͼÏó£¬Èôg£¨¦Á£©=$\frac{\sqrt{2}}{3}$+1£¬¦ÁΪµÚÒ»ÏóÏÞ£¬Çósin2¦ÁµÄÖµ£®

·ÖÎö £¨1£©¸ù¾ÝÁ½ÏòÁ¿µÄ×ø±ê£¬ÇóµÃº¯ÊýµÄ½âÎöʽ£¬½ø¶øÀûÓöþ±¶½Ç¹«Ê½ºÍÁ½½ÇºÍ¹«Ê½»¯¼òÕûÀíÇóµÃº¯ÊýµÄ½âÎöʽ£¬ÀûÓÃÕýÏÒº¯ÊýµÄµ¥µ÷ÐÔÇóµÃº¯ÊýµÄµ¥µ÷Çø¼ä£®
£¨2£©ÀûÓÃÆ½ÒƹæÂÉ£º¡°×ó¼ÓÓÒ¼õ¡±£¬È·¶¨³öf£¨x£©Æ½ÒƺóµÄ½âÎöʽg£¨x£©£¬¸ù¾Ýg£¨¦Á£©µÄÖµÁгö¹ØÏµÊ½£¬ÕûÀíºóµÃ³ösin£¨2¦Á-$\frac{¦Ð}{4}$£©µÄÖµ£¬ÓɦÁΪµÚÒ»ÏóÏ޽ǣ¬µÃ³ö2¦Á-$\frac{¦Ð}{4}$µÄ·¶Î§£¬ÔÙ¸ù¾Ýsin£¨2¦Á-$\frac{¦Ð}{4}$£©µÄ·¶Î§£¬ÀûÓÃͬ½ÇÈý½Çº¯Êý¼äµÄ»ù±¾¹ØÏµÇó³öcos£¨2¦Á-$\frac{¦Ð}{4}$£©µÄÖµ£¬½«ËùÇóʽ×ÓÖеĽÇ2¦Á±äÐÎΪ£¨2¦Á-$\frac{¦Ð}{4}$£©+$\frac{¦Ð}{4}$£¬ÀûÓÃÁ½½ÇºÍÓë²îµÄÕýÏÒº¯Êý¹«Ê½¼°ÌØÊâ½ÇµÄÈý½Çº¯ÊýÖµ»¯¼òºó£¬½«¸÷×ÔµÄÖµ´úÈë¼´¿ÉÇó³öÖµ£®

½â´ð ½â£º£¨1£©f£¨x£©=$\overrightarrow{m}•\overrightarrow{n}$=2sinxcosx+2cos2x
=sin2x+cos2x+1
=$\sqrt{2}$sin£¨2x+$\frac{¦Ð}{4}$£©+1
µ±2k¦Ð-$\frac{¦Ð}{2}$¡Ü2x+$\frac{¦Ð}{4}$¡Ü2k¦Ð+$\frac{¦Ð}{2}$£¬¼´k¦Ð-$\frac{3¦Ð}{8}$¡Üx¡Ük¦Ð+$\frac{¦Ð}{8}$£¨k¡ÊZ£©
¡àº¯ÊýµÄµ¥µ÷µÝÔöÇø¼äΪ[k¦Ð-$\frac{3¦Ð}{8}$£¬k¦Ð+$\frac{¦Ð}{8}$]£¨k¡ÊZ£©£®
£¨2£©¡ß½«º¯Êýy=f£¨x£©Í¼ÏóÏòÓÒÆ½ÒÆ$\frac{¦Ð}{4}$¸öµ¥Î»ºó£¬µÃµ½º¯Êýy=g£¨x£©=$\sqrt{2}$sin[2£¨x-$\frac{¦Ð}{4}$£©+$\frac{¦Ð}{4}$]+1=$\sqrt{2}$sin£¨2x-$\frac{¦Ð}{4}$£©+1£¬
¡à$\sqrt{2}$sin£¨2¦Á-$\frac{¦Ð}{4}$£©+1=$\frac{\sqrt{2}}{3}$+1£¬½âµÃ£ºsin£¨2¦Á-$\frac{¦Ð}{4}$£©=$\frac{1}{3}$£¬
¡ß¦ÁΪµÚÒ»ÏóÏÞ£¬
¡à2¦Á-$\frac{¦Ð}{4}$¡Ê£¨4k¦Ð-$\frac{¦Ð}{4}$£¬4k¦Ð+$\frac{3¦Ð}{4}$£©£¬k¡ÊZ£¬
ÓÖ0£¼sin£¨2¦Á-$\frac{¦Ð}{4}$£©£¼$\frac{1}{3}$£¼$\frac{\sqrt{2}}{2}$Öª£¬
¡à2¦Á-$\frac{¦Ð}{4}$¡Ê£¨4k¦Ð£¬4k¦Ð+$\frac{¦Ð}{2}$£©£¬k¡ÊZ£¬
¡àcos£¨2¦Á-$\frac{¦Ð}{4}$£©=$\frac{2\sqrt{2}}{3}$£¬
¡àsin2¦Á=sin[£¨2¦Á-$\frac{¦Ð}{4}$£©+$\frac{¦Ð}{4}$]=sin£¨2¦Á-$\frac{¦Ð}{4}$£©cos$\frac{¦Ð}{4}$+cos£¨2¦Á-$\frac{¦Ð}{4}$£©sin$\frac{¦Ð}{4}$=$\frac{\sqrt{2}}{2}£¨\frac{1}{3}+\frac{2\sqrt{2}}{3}£©$=$\frac{\sqrt{2}+4}{6}$£®

µãÆÀ ´ËÌ⿼²éÁËÊýÁ¿»ýµÄ×ø±ê±í´ïʽ¡¢¶þ±¶½ÇµÄÕýÏÒ¡¢ÓàÏÒº¯Êý¹«Ê½£¬Á½½ÇºÍÓë²îµÄÕýÏÒº¯Êý¹«Ê½£¬ÕýÏÒº¯ÊýµÄ¶¨ÒåÓòÓëÖµÓò£¬Èý½Çº¯ÊýͼÏóµÄ±ä»»£¬ÒÔ¼°ÕýÏÒº¯ÊýµÄµ¥µ÷ÐÔ£¬ÊìÁ·ÕÆÎÕ¹«Ê½ÊǽⱾÌâµÄ¹Ø¼ü£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®ÒÑÖªÇúÏßf£¨x£©=ax2+blnxÔÚx=1´¦µÄÇÐÏß·½³Ì4x-2y-3=0£¬Çóa£¬b£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

18£®ÔÚijÏî²âÁ¿ÖУ¬Ä³ÏîÖ¸±êÏàÓ¦µÄËæ»ú±äÁ¿¦Î·þ´Ó±ê×¼Õý̬·Ö²¼N£¨0£¬1£©£¬ÈôP£¨|¦Î|£¼1.96£©=0.950£¬Ôò¦ÎÔÚ£¨-¡Þ£¬1.96£©ÄÚȡֵµÄ¸ÅÂÊΪ0.975£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®ÒÑÖªÆ½ÃæÖ±½Ç×ø±êϵxOyÖУ¬¶¯µãMµ½¶¨µãA£¨1£¬0£©£¬B£¨4£¬0£©µÄ¾àÀëÖ®±ÈΪ$\frac{1}{2}$£¬É趯µãMµÄ¹ì¼£ÎªÇúÏßC£®
£¨¢ñ£©ÇóÇúÏßCµÄ·½³Ì£»
£¨¢ò£©¹ýµãB×÷бÂÊΪ0µÄÖ±ÏßlÓëÇúÏßCÏཻÓÚP£¬QÁ½µã£»
£¨¢¡£©ÈôOP¡ÍOQ£¬ÇóÖ±ÏßlµÄ·½³Ì£»
£¨¢¢£©ÇóÈý½ÇÐÎAPQÃæ»ýµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

2£®ÇóÖ¤£º-$\frac{1}{2}$¡Üx$\sqrt{1-{x}^{2}}$¡Ü$\frac{1}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

12£®Å×ÎïÏßy=-x2+3x-6ÉÏËùÓеãµÄ¼¯ºÏΪ{£¨x£¬y£©|y=-x2+3x-6}£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

19£®ÏÂÁи÷×麯ÊýÊÇͬһº¯ÊýµÄÊÇ£¨2£©
£¨1£©f£¨x£©=$\sqrt{x+1}$$\sqrt{x-1}$£¬g£¨x£©=$\sqrt{£¨x+1£©£¨x-1£©}$£»
£¨2£©f£¨x£©=x2-2x-1Óëg£¨t£©=t2-2t-1£»
£¨3£©f£¨x£©=$\sqrt{-2{x}^{3}}$Óëg£¨x£©=x$\sqrt{-2x}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®¶¨ÒåÔÚRÉϵÄżº¯Êýf£¨x£©ÔÚ£¨-¡Þ£¬0]ÉÏÊǵ¥µ÷Ôöº¯Êý£¬Ôò²»µÈʽf£¨x+2£©-f£¨2x+1£©£¾0µÄ½â¼¯Îª£¨-¡Þ£¬-1£©¡È£¨1£¬+¡Þ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®ÒÑÖªtan¦Á=-$\frac{1}{3}$£®
£¨1£©$\frac{4sin¦Á-2cos¦Á}{5cos¦Á+3sin¦Á}$£»
£¨2£©£¨sin¦Á-cos¦Á£©2£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸