# [pdf]

(0,0)
f(x, y) = x3
y
f(x, y) = x+2y
x2y2
f(x, y) = x2+y2
|x|+|y|
(0,0)
f(x, y) = x3+y3
x2+y2
f(x, y) = xy
x4+y4
f(x, y) = x2y
x4+y2
f(x, y) = xy
xy
(0,0)
f(x, y) = sin xy
x2+y2
f(x, y) = 1cos(xy)
xy2
f(x, y) = xy= eyln x
f(x, y) = sh xsh y
x+y
f:R+×R
+Rf(x, y) = xyx > 0f(0, y)=0
f
R+×R+
f:RRC1F:R2\ {(0,0)} → R
F(x, y) = f(x2+y2)f(0)
x2+y2
lim(x,y)(0,0) F(x, y)
f(0,1/n)0f(1/n, 1/n3)1 (0,0)
f(0,1/n)=2n+f(0,1/n) = 2n→ −∞ (0,0)
0f(x, y)x2+2|x||y|+y2
|x|+|y|=|x|+|y| → 0f(rcos θ, r sin θ) = O(r)
x=rcos θ y =rsin θ r =px2+y20
f(x, y) = r(cos3θ+ sin3θ)
(x,y)(0,0) 0
f(1/n, 0) 0f(1/n, 1/n3)1f(0,0)
f(1/n, 0) = 0 0f(1/n, 1/n2)=1/21/2f
(0,0)
f(1/n, 0) = 0 0f(1/n + 1/n2,1/n) = 1/n2+1/n3
1/n21f
(0,0)
|f(x, y)| ≤ |xy|
x2+y2=r|sin θcos θ| −
(x,y)(0,0) 0
f(x, y) = x1cos(xy)
x2y2limt01cos t
t2=1
2f(x, y)
(x,y)(0,0) 0
f(1/n, 0) 1f(1/n, 1/ln n)1/e (0,0)
x0f(x, x+x3)∼ −1
xf(0,0)
f(x, y) = exp(yln x)R
+×R
+
(0, b)b > 0
(x, y)(0, b) (x, y)R
+×R
+yln x→ −∞
f(x, y) = xy0
(0, y)(0, b)f(x, y) = 0 0
f(0, b)
fR+×R+
f(0,0) = limy0f(0, y) = 0
f(0,0) = limx0f(x, x)=1
cx,y ]0 ; x2+y2[
F(x, y) = f0(c)
(x, y)(0,0) cx,y 0F(x, y)f0(0)
1 / 2 100%

# [pdf]

##### Documents connexes
La catégorie de ce document est-elle correcte?
Merci pour votre participation!

### Faire une suggestion

Avez-vous trouvé des erreurs dans linterface ou les textes ? Ou savez-vous comment améliorer linterface utilisateur de StudyLib ? Nhésitez pas à envoyer vos suggestions. Cest très important pour nous !