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f : D → R
D ⊆ Rn γ : [a, b] → D a, b ∈ R
a < b γ(a) γ(b) x0 f ◦ γ : [a, b] → R
γ(b) = x0 lim
x→x0
x∈D
γ(a) = x0 lim
x→x0
x∈D
lim
t→b
f(x) lim f ◦ γ(t),
t→b− f(x) lim f ◦ γ(t),
t→a +
t→a
f ◦ γ(t), lim f ◦ γ(t),
− +
γ
f : D → R D ⊆ Rn c D
lim f(x, y) ℓ
x→c
x∈D
{xn}n∈N ⊆ D xn → c lim
n→∞ f(xn) = ℓ
γ : [a, b[→ D lim
t→b
t→b
γ(t) = c lim f(t) = ℓ
− −
f : D → R D ⊆ R2 (x0, y0)
D ε > 0 ] − ε, ε[×{y0} ∪ {x0}×] − ε, ε[⊂ D lim f(x, y)
lim
y→y0
lim f(x, y)
x→x0
= lim
x→x0
lim f(x, y)
y→y0
= lim
f(x, y) =
(x,y)→(x0,y0)
(x,y)∈D
(x,y)→(x0,y0)
(x,y)∈D
f(x, y),
x 2
x 2 + y 2 D = R2 \ {(0, 0)} m ∈ R x > 0
γm : [0, x] → D γm(t) = (t, mt) γm
[0, x] R t = 0 γ(t) ∈ D
lim f ◦ γ(t) = lim f(t, mt) = lim
t→a + t→0 + t→0 +
t2 t2 + m2 1
= .
t2 1 + m2 m γm
γm m m f
γm
f(x, y) = xy2
x 2 + y 4 D = R \ {(0, 0)} γm(t) = (t, mt)
lim
t→0
f ◦ γ(t) = lim f(t, mt) = lim
t→0 t→0
m2t3 t2 + m4 = lim
t4 t→0
m2t 1 + m2 = 0,
t2 m γ+(t) = (t 2 , t)
γ−(t) = (−t 2 , t)
lim
t→0 f ◦ γ+(t) = lim f(t
t→0 2 t
, t) = lim
t→0
4
t4 1
=
+ t4 2 ,
lim
t→0 f ◦ γ−(t) = lim f(−t
t→0 2 −t
, t) = lim
t→0
4
t4 = −1
+ t4 2 ,
f
(x, y) → (0, 0)