Limites al infinito: propiedades
· Lim k = 0 X →∞
· Lim k = 0 X → + ∞
· Lim k = 0 X → - ∞
· Lim 1 = 0 X → ∞ x
- 2x + 5
· Lim = lim
X → +∞ 8 x → +∞ 8
= lim 1 - 2 + 5
x →+∞ x
8 + 1 + 2
X - 9
· Lim x - 9 = x x .
X →∞
9
= lim 1 - x .
X → ∞ + 3 + 2
X
= lim 1 .
X →∞
= 1
2
(
· Lim = lim x .
X → ∞ x x → ∞ x
x
(
= lim x .
X→∞ 1
= 0
1
= 0
LN = logaritmo natural = ln ( 10 )
1.) Lim ( ln x – x + cos x)
X→10
= lim ln x – lim x + lim cos x
X→10 x→10 x →10
= - 8.53
2.) Lim 1 = 0.11920
X→2 1 +
3.) Lim
X →2 ( 2 + 3
= 26,77
4.) Lim
X →π ( cos 3 x + 1 sen 2 x + tan x ) = 0.00000
2 4
5.) Lim
X →3
=
10
= 126
DERIVE
Y = 3 - 5
Y = 0 3.2 - 0
Y` = 6x = f (x) = 6x = dx = 6x
dx
y = k
y = k
y = k y = f (x)
y`= 0
y`= f`(x)= dy
dx
f(x) = 1 - - - x + π
2
f`(x) = 1 . 4 - 1 . 3 - 1 . 2 - 1 . 1
2
F`(x) = 2 - 3 -2x -1x
F`(x) = 2 - 2x -1
Y = 2 + x + e
2
Y = 2 + 1 x + e
2
Y`= 2 . 1 + 1 . 1 +0
2 2
Y`= + 1
2
Interpretacion geometrica de la derivada
M = Δy = yf – yi = y1 – y 2 = f (x1) f ( x2)
Δx xf - xi = x1 – x 2 = x1 - x 2
La derivada de una function es la pendiente (inclinacion) de la recta tangent a una curva en u punto.
Lim m sec = lim f ( x + h ) + f ( x )
H→0 h→0 h
= f`(x) ly = m tan = Y`
lx
hallar la pendiente de la recta tangente (derivada) de la función: luego hallar la recta tangente en el punto ( 3 , 4 )
f(x) =
= lim [( x + h [
H →0 h
= lim
H →0 h
=lim 2xh + - 2h
H→0 h
=lim h ( 2x + h – 2 )
H→0 h
=lim ( 2x + h – 2 )
H →0
