绗崄鍏珷
澶氬厓鍑芥暟鐨勬瀬闄愪笌杩炵画
绗竴鑺?/p>
骞抽潰鐐归泦涓庡鍏冨嚱鏁?/p>
1
銆佸垽鏂笅鍒楀钩闈㈢偣闆嗕腑鍝簺鏄紑闆嗐�侀棴闆嗐�佹湁鐣岄泦銆佸尯鍩燂紝骞跺垎鍒寚鍑哄畠浠殑
鑱氱偣涓庣晫鐐癸細
(1)[a,b)
脳
[c,d)
锛?/p>
(2){(x,y)|xy
鈮?/p>
0}
锛?/p>
(3){(x,y)|xy=0}
锛?/p>
(4){(x,y)|y>x
2
}
锛?/p>
(5){(x,y)|x<2,y<2,x+y>2}
锛?/p>
(6){(x,y)|x
2
+y
2
=1
鎴?/p>
y=0,0
鈮?/p>
x
鈮?/p>
1}
(7){(x,y)|x
2
+y
2
鈮?/p>
1
鎴?/p>
y=0,1
鈮?/p>
x
鈮?/p>
2}
(8){(x,y)|x,y
鍧囦负鏁存暟
}
锛?/p>
(9){(x,y)|y=sin
1
x
,x>0}.
2
銆?/p>
璇曢棶闆嗗悎
{(x,y)|0<|x-a|<
未
,0<|y-b|<
未
}
涓庨泦鍚?/p>
{(x,y)||x-a|<
未
,|y-b|<
未
,(x,y)
鈮?/p>
(a,b)}
鏄惁鐩稿悓锛?/p>
3
銆佽瘉鏄庯細褰撲笖浠呭綋瀛樺湪鍚勭偣浜掍笉鐩稿悓鐨勭偣鍒?/p>
{P
n
}
鈯?/p>
E
锛?/p>
P
n
鈮?/p>
P
0
,
lim
x
P
n
=P
0
鏃讹紝
P
0
鏄?/p>
E
鐨勮仛鐐?/p>
.
4
銆佽瘉鏄庯細闂煙蹇呬负闂泦
.
涓句緥璇存槑鍙嶄箣
.
涓嶇湡
.
5
銆佽瘉鏄庯細鐐瑰垪
{P
n
(x
n
,y
n
)}
鏀舵暃浜?/p>
P
0
(x
0
,y
0
)
鐨勫厖瑕佹潯浠舵槸
lim
x
x
n
=x
0
鍜?/p>
lim
x
y
n
=y
0.
6
銆佹眰涓嬪垪鍚勫嚱鏁扮殑鍑芥暟鍊硷細
锛?/p>
1
锛?/p>
f(x,y)=[
arctan(x+y)
arctan(x-y)
]
2
锛屾眰
f(
1+
3
2
,
1-
3
2
)
锛?/p>
锛?/p>
2
锛?/p>
f(x,y)=
2xy
x
2
+y
2
锛屾眰
f(1,
y
x
)
锛?/p>
锛?/p>
3
锛?/p>
f(x,y)=x
2
+y
2
-xytan
x
y
锛屾眰
f(tx,ty).
7
銆佽
F(x,y)=ln xln y,
璇佹槑锛氳嫢
u>0,v>0,
鍒?/p>
F(xy,uv)=F(x,u)+F(x,v)+F(y,u)+F(y,v).
8
銆佹眰涓嬪垪鍚勫嚱鏁扮殑瀹氫箟鍩燂紝鐢诲嚭瀹氫箟鍩熺殑鍥惧舰锛屽苟璇存槑鏄綍绉嶇偣闆嗭細
锛?/p>
1
锛?/p>
f(x,y)=
x
2
+y
2
x
2
-y
2
锛?/p>
锛?/p>
2
锛?/p>
f(x,y)=
1
2x
2
+3y
2
锛?/p>
锛?/p>
3
锛?/p>
f(x,y)=
xy
锛?/p>
锛?/p>
4
锛?/p>
f(x,y)=
1-x
2
+
y
2
-1
锛?/p>
锛?/p>
5
锛?/p>
f(x,y)=ln x+ln y
锛?/p>
锛?/p>
6
锛?/p>
f(x,y)=
sin(x
2
+y
2
)
锛?/p>
锛?/p>
7
锛?/p>
f(x,y)=ln (y-x)
锛?/p>
锛?/p>
8
锛?/p>
f(x,y)=e
-(x
2
+y
2
)
锛?/p>
9
锛?/p>
f(x,y,z)=
z
x
2
+y
2
+1
锛?/p>