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涓撻
13
瀵兼暟鐨勬蹇靛強鍏惰繍绠?/p>
1.
浜嗚В瀵兼暟姒傚康鐨勫疄闄呰儗鏅紱
2.
閫氳繃鍑芥暟鍥捐薄鐩磋鐞嗚В瀵兼暟鐨勫嚑浣曟剰涔夛紱
3.
鑳芥牴鎹鏁扮殑瀹氫箟姹傚嚱鏁?/p>
y
锛?/p>
c(c
涓哄父鏁?/p>
)
锛?/p>
y
锛?/p>
x
锛?/p>
y
锛?/p>
1
x
锛?/p>
y
锛?/p>
x2
锛?/p>
y
锛?/p>
x3
锛?/p>
y
锛?/p>
x
鐨勫鏁帮紱
4.
鑳藉埄鐢ㄥ熀鏈垵绛夊嚱鏁扮殑瀵兼暟鍏紡鍜屽鏁扮殑鍥涘垯杩愮畻娉曞垯姹傜畝鍗曞嚱鏁扮殑瀵兼暟锛岃兘姹傜畝鍗曞鍚?/p>
鍑芥暟
(
浠呴檺浜庡舰濡?/p>
y
锛?/p>
f(ax
锛?/p>
b)
鐨勫鍚堝嚱鏁?/p>
)
鐨勫鏁帮紟
1
锛庡嚱鏁?/p>
f(x)
鍦ㄧ偣
x0
澶勭殑瀵兼暟
(1)
瀹氫箟
鍑芥暟
y
锛?/p>
f(x)
鍦ㄧ偣
x0
鐨勭灛鏃跺彉鍖栫巼
lim
螖
x鈫?/p>
0
f
飥▁0锛?/p>
螖
x飥紞
f
飥▁0飥?
螖
x
锛?/p>
l
锛岄�氬父绉颁负
f(x)
鍦ㄧ偣
x0
澶勭殑瀵兼暟锛屽苟璁颁綔
f鈥?x0)锛屽嵆
lim
螖
x鈫?
f
飥▁0锛?/p>
螖
x飥紞
f
飥▁0飥?
螖
x
锛漟鈥?x0)锛?/p>
(2)
鍑犱綍鎰忎箟
鍑芥暟
f(x)
鍦ㄧ偣
x0
澶勭殑瀵兼暟
f鈥?x0)鐨勫嚑浣曟剰涔夋槸鏇茬嚎
y
锛?/p>
f(x)
鍦ㄧ偣
(x0
锛?/p>
f(x0))
鐨勫垏绾跨殑鏂滅巼
绛変簬
f鈥?x0)锛?/p>
2
锛庡嚱鏁?/p>
f(x)
鐨勫鍑芥暟
濡傛灉
f(x)
鍦ㄥ紑鍖洪棿
(a
锛?/p>
b)
鍐呮瘡涓�鐐?/p>
x
瀵兼暟閮藉瓨鍦紝鍒欑О
f(x)
鍦ㄥ尯闂?/p>
(a
锛?/p>
b)
鍙锛庤繖鏍凤紝瀵瑰紑
鍖洪棿
(a
锛?/p>
b)
鍐呮瘡涓�?/p>
x
锛岄兘瀵瑰簲涓�涓‘瀹氱殑瀵兼暟
f鈥?x)锛庝簬鏄紝鍦ㄥ尯闂?/p>
(a
锛?/p>
b)
鍐咃紝f鈥?x)鏋?/p>
鎴愪竴涓柊鐨勫嚱鏁帮紝鎴戜滑鎶婅繖涓嚱鏁扮О涓哄嚱鏁?/p>
y
锛?/p>
f(x)
鐨勫鍑芥暟锛岃涓?/p>
f鈥?x)(鎴?/p>
y鈥瞲銆亂鈥?锛?/p>
3
锛庡熀鏈垵绛夊嚱鏁扮殑瀵兼暟鍏紡
y
锛?/p>
f(x)
y鈥诧紳f鈥?x)
y
锛?/p>
C
y
锛?/p>
xn
y
锛?/p>
x
渭
(x>0
锛?/p>
渭
鈮?)
y
锛?/p>
ax (a>0
锛宎鈮?)
y
锛?/p>
ex
y
锛?/p>
logax(a>0
锛宎鈮?锛?/p>
x>0)
y
锛?/p>
ln x
y
锛?/p>
sin x
y
锛?/p>
cos x
y鈥诧紳
0
y鈥诧紳
nxn
锛?/p>
1
锛?/p>
n
涓鸿嚜鐒舵暟
y鈥诧紳
渭
x
渭
锛?/p>
1
锛?/p>
渭
涓烘湁鐞嗘暟
y鈥诧紳
axln a
y鈥诧紳
ex
y鈥诧紳
1
xln a
y鈥诧紳
1
x
y鈥诧紳
cos x
y鈥诧紳锛?/p>
sin x
4
锛庡鏁扮殑杩愮畻娉曞垯
(1)[f(x)卤g(x)]鈥诧紳f鈥?x)卤g鈥?x)锛?/p>
(2)[f(x)路g(x)]鈥诧紳f鈥?x)g(x)锛媐(x)g鈥?x)锛?/p>