Sol:
(x,y)+(1,1) e te
xy?
lim
(x,y)(0,0) x? +
(99 台聯大)
2
,2
- :
<範例>: Find the linait
Sol:
xz2
0
= lim
y no 0+ y?
12
<1> #x+0,#y+0= FIT = lim lim
yo xo x²
ty
buya
0
=
<2> 先y→0,
再入→0原式= lim lim
lim
= 0
x>0
y~0 x + y
x>0
x +0
X
<3> 次方:令y=x">原式= lim
2m-1
x
2m+1
x
lim
x+0 x² + x
2m
-
= lim
x0
2 2
X +
0 = 0
2m-2
(z") ?
xo 1+x
(rcos O)(rsin 6)?
<4> 極座標→原式= im
ro
p2
0任意
lim r cos Osin? 0 = 0
r0
0任意
綜合上述: lim
(x,y)==(0,0) x² + y^
?
xya
= 0
