8/18/2019 Muturrak5Gaia
1/2
a f
∃ δ > 0 /
f (x) ≤ f (a)f (x) ≥ f (a)
∀x ∈ (a − δ, a + δ ) .
f a f (a) = 0
limx→a
f [a, b] (a, b) f (a) = f (b)
∃c ∈ (a, b) / f (c) = 0 .
f
[a, b] (a, b)
∃c ∈ (a, b) / f (c) = f (b) − f (a)
b − a .
f f
f
g
f (x) =g (x) = 0
∃k / f (x) = g (x) + k .
f g [a, b] (a, b) g (x) = 0
∃c ∈ (a, b) / f (c)
g (c) =
f (b) − f (a)
g (b) − g (a) .
8/18/2019 Muturrak5Gaia
2/2
limx→a
f (x)g(x) =
00
limx→a
f (x) = limx→a
g (x) =
0 limx→a
f (x)g(x)
limx→a
f (x)g(x)
limx→a
f (x)
g (x) = lim
x→a
f (x)
g (x) .
• limx→a
f (x) = limx→a
g (x) = ±∞ ∞∞
• limx→±∞
f (x)g(x)
1t
• limx→a
f (x)g(x) = ±∞
• 0 · ∞
• ∞ − ∞
• 00, ∞0, 1∞
Recommended