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Ingeniería Matemática
FACULTAD DE CIENCIAS
FÍSICAS Y MATEMÁTICAS
UNIVERSIDAD DE CHILE
Introducción al Cálculo 08-1
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78
lı́m x = 02
x→0
98
:8
;8
<8
=8
lı́m x = 02
x→0+
1
x
lı́m
1
ln(x)
lı́m
1
| ln(x)|
lı́m 1 −
x→0+
x→0+
1
lı́m e x
x→0−
>8
lı́m
x→0−
?8
= 02
x→1
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= +∞2
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√
−x
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4'#' "0+' 5.&*%6& f ,% x→x
lı́m
lı́m 2f (x) = 2 + u2
x→x
f (x) = u
0
0
@8
7A8
1
lı́m
2
x→0+ ln(x )
= 22
lı́m ln(x2 ) = +∞2
x→0
778
lı́m ex = 02
x→0
798
lı́m ln(x) = 12
x→1
7:8
lı́m sen(x) = 02
x→0
7;8
lı́m e · ex = 02
x→−1
lı́m ln( xe ) = 02
7<8
x→e
7=8
x→π
lı́m sen(π − x) = 12
789
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456
476
lı́m xex = 0
x→+∞
lı́m ax = 0
x→0
486
1
lı́m x x = 0
x→0
9:6
lı́m xx = 1
x→0
946
996
lı́m sen(x) = +∞
x→+∞
lı́m tan(x) = 1
x→0
9;6
9<6
x→0
ex −e−x
2
lı́m
√
x=0
lı́m
=1
x→0
9=6
lı́m
√
x=2
x→1
9>6
lı́m log2 (x) = 3
x→8
956
976
lı́m ln(x) = 1
x→e
lı́m exp(x) = −e4
x→−4
986
;:6
lı́m 3+4x2
x→−4 6−x
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lı́m log3 (x) +
√
x=5
x→9
;46
x→π
;96
x→+∞
;;6
x→+∞
;<6
;=6
lı́m cos(x) + sen(x) = −1
lı́m x + ln(x) = 0
lı́m x2 + ln(x) = +∞
lı́m (1 + x2 ) · ln(x) = −∞
x→0+
lı́m
x→0
;>6
;56
sen(x)
x
=0
lı́m
ex −1
x
lı́m
ln(1+x)
x
x→0+
=1
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x→0−
()*