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Ô²
ÓÐÒ»Ô², Æä°ë¾¶ÒÔÿÃë ÀåÃ׵͍ËÙ¶ÈÔö¼Ó. µ±°ë¾¶µÈÓÚ ÀåÃ×ʱ, ËüµÄÃæ»ýÔö¼ÓµÄËÙ¶ÈÈçºÎ (ÒÔ cm2/s Ϊµ¥Î»)?
Ô² II
ÓÐÒ»Ô², Æä°ë¾¶ÒÔÿÃë ÀåÃ׵͍ËÙ¶ÈÔö¼Ó. µ±Ãæ»ýµÈÓÚ Æ½·½ÀåÃ×ʱ, ËüµÄÃæ»ýÔö¼ÓµÄËÙ¶ÈÈçºÎ (ÒÔ cm2/s Ϊµ¥Î»)?
Ô² III
ÓÐÒ»Ô², ÆäÃæ»ýÒÔÿÃë Æ½·½ÀåÃ׵͍ËÙ¶ÈÔö¼Ó. µ±Ãæ»ýµÈÓÚ Æ½·½ÀåÃ×ʱ, ËüµÄ°ë¾¶Ôö¼ÓµÄËÙ¶ÈÈçºÎ (ÒÔ cm/s Ϊµ¥Î»)?
Ô² IV
ÓÐÒ»Ô², ÆäÃæ»ýÒÔÿÃë Æ½·½ÀåÃ׵͍ËÙ¶ÈÔö¼Ó. µ±°ë¾¶µÈÓÚ ÀåÃ×ʱ, ËüµÄ°ë¾¶Ôö¼ÓµÄËÙ¶ÈÈçºÎ (ÒÔ cm/s Ϊµ¥Î»)?
¸´ºÏ I
ÓÐÁ½¸ö¿É΢º¯Êý f(x) Óë g(x), Æäµ¼ÊýÖµÈçϱíËùʾ. x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
f(x) | | | | | | | |
f '(x) | | | | | | | |
g(x) | | | | | | | |
g'(x) | | | | | | | |
Éè h(x) = f(g(x)). ¼ÆËãµ¼Êý h'().
¸´ºÏ II *
ÓÐ 3 ¸ö¿É΢º¯Êý f(x), g(x) Óë h(x), Æäµ¼ÊýÖµÈçϱíËùʾ. x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
f(x) | | | | | | | |
f '(x) | | | | | | | |
g(x) | | | | | | | |
g'(x) | | | | | | | |
h(x) | | | | | | | |
h'(x) | | | | | | | |
Éè s(x) = f(g(h(x))). ¼ÆËãµ¼Êý s'().
»ìºÏ¸´ºÏ
ÓÐÒ»¸ö¿É΢º¯Êý f(x), Æäº¯ÊýÖµºÍµ¼ÊýÖµÈçϱíËùʾ. Éè g(x) = , ÇÒÉè h(x) = g(f(x)). ¼ÆËãµ¼Êý h'().
Á´Ìõ¼þ Ia
Éè
ÊÇ¿É΢º¯Êý, µ¼º¯ÊýÊÇ
. ¼ÆËã
µÄµ¼º¯Êý.
Á´Ìõ¼þ Ib
Éè
ÊÇ¿É΢º¯Êý, µ¼º¯ÊýÊÇ
. ¼ÆËã
µÄµ¼º¯Êý.
³ý·¨ I
ÓпÉ΢º¯Êý f(x) Óë g(x), ÆäÖµÓëµ¼ÊýÈçϱíËùʾ. x | -2 | -1 | 0 | 1 | 2 |
f(x) | | | | | |
f '(x) | | | | | |
g(x) | | | | | |
g'(x) | | | | | |
Éè h(x) = f(x)/g(x). ¼ÆËãµ¼Êý h'().
»ìºÏ³ý·¨
ÓпÉ΢º¯Êý f(x), ÆäÖµÓëµ¼ÊýÈçϱíËùʾ. Éè h(x) = / f(x). ¼ÆËãµ¼Êý h'().
Ë«Çúº¯Êý I
¼ÆËãÒÔϺ¯ÊýµÄµ¼Êý f(x) = .
Ë«Çúº¯Êý II
³Ë·¨ I
ÓÐÁ½¸ö¿É΢º¯Êý f(x) Óë g(x), ÆäÖµºÍµ¼ÊýÈçϱíËùʾ. x | -2 | -1 | 0 | 1 | 2 |
f(x) | | | | | |
f '(x) | | | | | |
g(x) | | | | | |
g'(x) | | | | | |
Éè h(x) = f(x)g(x). ¼ÆËãµ¼Êý h'().
³Ë·¨ II
ÓÐÁ½¸ö¿É΢º¯Êý f(x) Óë g(x), ÆäÖµºÍµ¼ÊýÈçϱíËùʾ. x | -2 | -1 | 0 | 1 | 2 |
f(x) | | | | | |
f '(x) | | | | | |
f ''(x) | | | | | |
g(x) | | | | | |
g'(x) | | | | | |
g''(x) | | | | | |
Éè h(x) = f(x)g(x). ¼ÆËã¶þ½×µ¼Êý h''().
»ìºÏ³Ë·¨
ÓпÉ΢º¯Êý f(x), ÆäÖµºÍµ¼ÊýÈçϱíËùʾ. Éè h(x) = f(x). ¼ÆËãµ¼Êý h'().
¹ãÒå³Ë·¨ I
Éè
Êǵ¼º¯ÊýΪ
µÄ¿É΢º¯Êý. ¼ÆËã
µÄµ¼º¯Êý.
¶àÏîʽ I
¼ÆËãÒÔϺ¯ÊýµÄµ¼Êý f(x) = , ¶Ô x=.
¶àÏîʽ II
¼ÆËãÒÔϺ¯ÊýµÄµ¼Êý
.
ÓÐÀíº¯Êý I
ÓÐÀíº¯Êý II
Äæº¯ÊýµÄµ¼Êý
Éè : -> ÊÇÓÉÏÂʽ¶¨ÒåµÄº¯Êý (x) = . ÑéÖ¤ ÊÇË«Éä, ËùÒÔÓÐÄæº¯Êý (x) = -1(x). ¼ÆËãµ¼ÊýµÄÖµ '() .
ÄãµÄ»Ø´ðÖÁÉÙÓ¦ÓÐ 4 λÓÐЧÊý×Ö.
³¤·½ÐÎ I
ÓÐÒ»¸ö³¤·½ÐÎ, ËüµÄÒÔÿÃë ÀåÃ׵͍ËÙ, µ«ÊÇËüµÄ±£³Ö²»±ä, Ϊ . µ±µÈÓÚ Ê±, ±ä»¯µÄËÙ¶È (ÒÔ Îªµ¥Î») ÊǶàÉÙ?
³¤·½ÐÎ II
ÓÐÒ»¸ö³¤·½ÐÎ, ËüµÄÒÔÿÃë ÀåÃ׵͍ËÙ, µ«ÊÇËüµÄ±£³Ö²»±ä, Ϊ . µ±µÈÓÚ Ê±, ±ä»¯µÄËÙ¶È (ÒÔ Îªµ¥Î») ÊǶàÉÙ?
³¤·½ÐÎ III
ÓÐÒ»¸ö³¤·½ÐÎ, ËüµÄÒÔÿÃë ÀåÃ׵͍ËÙ, µ«ÊÇËüµÄ±£³Ö²»±ä, Ϊ . µ±µÈÓÚ Ê±, ±ä»¯µÄËÙ¶È (ÒÔ Îªµ¥Î») ÊǶàÉÙ?
³¤·½ÐÎ IV
ÓÐÒ»¸ö³¤·½ÐÎ, ËüµÄÒÔÿÃë ÀåÃ׵͍ËÙ, µ«ÊÇËüµÄ±£³Ö²»±ä, Ϊ . µ±µÈÓÚ Ê±, ±ä»¯µÄËÙ¶È (ÒÔ Îªµ¥Î») ÊǶàÉÙ?
³¤·½ÐÎ V
ÓÐÒ»¸ö³¤·½ÐÎ, ËüµÄÒÔÿÃë ÀåÃ׵͍ËÙ, µ«ÊÇËüµÄ±£³Ö²»±ä, Ϊ . µ±µÈÓÚ Ê±, ±ä»¯µÄËÙ¶È (ÒÔ Îªµ¥Î») ÊǶàÉÙ?
³¤·½ÐÎ VI
ÓÐÒ»¸ö³¤·½ÐÎ, ËüµÄÒÔÿÃë ÀåÃ׵͍ËÙ, µ«ÊÇËüµÄ±£³Ö²»±ä, Ϊ . µ±µÈÓÚ Ê±, ±ä»¯µÄËÙ¶È (ÒÔ Îªµ¥Î») ÊǶàÉÙ?
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ÓÐÒ»¸öÖ±½ÇÈý½ÇÐÎ, ÆäÖÐ AB= , ÇÒ AC ÒÔ /s µÄ¶¨ËÙ¶È. µ± AC= ʱ, ÎÊ BC ±ä»¯µÄËÙ¶ÈÊÇʲô (ÒÔ /s Ϊµ¥Î»)?
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ÓÐÈËÒÔÿÃë Ã׵͍ËÙ¶ÈÏòÒ»×ùËþǰ½ø. Èç¹ûËþµÄ¸ß¶ÈÊÇ Ã×, µ±Õâ¸öÈËÓëËþµÄµ×²¿Ïà¾à Ã×ʱ, ´ËÈËÓëËþ¶¥¾àÀë¼õÉÙµÄËÙ¶ÈÊÇʲô (ÒÔ m/s Ϊµ¥Î»)?
Èý½Çº¯Êý I
¼ÆËãÒÔϺ¯ÊýµÄµ¼Êý f(x) = .
Èý½Çº¯Êý II
Èý½Çº¯Êý III
¼ÆËãÒÔϺ¯ÊýÔÚµã x= µÄµ¼Êý f(x) = .
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