Apunte de Calculo
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Transcript of Apunte de Calculo
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8/18/2019 Apunte de Calculo
1/5
f (x) = x2 f (1) = 1 x 1
x f (x)
x 1 f (x)
ĺımx→1
x2 = 1
x = 0, 9; 0, 99; 0, 999... f (x)
ĺımx→1−
x2 = 1
x = 1, 1; 1, 01; 1, 001... f (x)
ĺımx→1+
x2 = 1
ĺımx→2
4 − x2
f (x) = c ĺımx→a
f (x) = c
ĺımx→a
f (x) = A y ĺımx→a
g(x) = B
ĺımx→a
Kf (x) = KA; K = const
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8/18/2019 Apunte de Calculo
2/5
ĺımx→
a
f (x)
±g(x) = A
±B
ĺımx→a
f (x) · g(x) = A · B
ĺımx→a
f (x)
g(x) =
A
B
ĺımx→a
f (x) =
√ A
x = x0
f (x0)
ĺımx→x0
f (x)
ĺımx→x0
f (x) = f (x0)
f (x) = 1
x − 2 x = 2
f (x) = x2 − 4
x − 2 x = 2
ĺımx→0
y x
= ĺımx→0
f (x+ x) − f (x) x
y = f (x) x
dy
dx, y, f (x),
d
dxf (x)
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8/18/2019 Apunte de Calculo
3/5
f (x) = x2
dydx
= ĺımx→0
f (x+ x) − f (x) x
dy
dx = ĺım
x→0
(x+ x)2 − x2 x
= ĺımx→0
x2 + 2x x + ( x)2 − x2 x
= ĺımx→0
2x x + ( x)2
x
dy
dx = ĺım
x→02x+ x = 2x
d
dxc = 0
d
dxx = 1
d
dxxn = nxn−1
d
dxun = nun−1
d
dxu
d
dxcu = c
d
dxu
d
dxuv = u
d
dxv + v
d
dxu
d
dx
uv
=
v d
dxu − u d
dxv
v2
d
dxeu = eu
d
dxu
d
dxlnu =
1
u
d
dxu
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8/18/2019 Apunte de Calculo
4/5
f (x)dx
2x
2xdx = x2 + c
c
ba
f (x)dx
2x −2 ≤ x ≤ 1 1−2
2xdx =
x21−2
= (1)2 − (−2)2 = −3
ddx
f (x)dx = f (x) + c
undu =
un+1
n + 1 + c
1u
du = ln |u| + c
eudu = eu + c
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8/18/2019 Apunte de Calculo
5/5
m = dydx
y