Wydział ILiŚ, Budownictwo i Transport, sem.1

dr Jolanta Dymkowska Twierdzenie de L’Hospitala Zad.1 Oblicz granice funkcji: 1.1

lim

1

1.2

lim

x+1

1.3

lim arctg 2x

x→0 ex−1

x→∞

ln x

x→0

x2+3x

1.4

lim e3x−3x−1

1.5

lim x−arctg x

1.6

lim

ln x

√

x→0

sin2 5x

x→0

x3

x→∞

x2−1

√1−x

1.7

lim 1−cos x

1.8

lim x2−1+ln x

1.9

lim

e

−1

x→0

2x2

x→1

ex−e

sin(x−1)

x→1−

1.10

lim cos x − sin x + 1

1.11

lim

ln sin 2x

1.12

lim

ln ln x

x→ π

sin 2x − cos x

ln sin 3x

x

x→0+

x→∞

2

1.13

lim ex−e−x−2x

1.14

lim ex−1−e1−x−2x+2

x→0

x−sin x

x→1

x−1−sin(x−1)

1.15

lim

1 −

1

1.16

lim

1

−

1

1.17

lim

1

− ctg 2x

x→0

x

ex−1

x→1

ln x

x−1

x→0

x2

√

1.18

lim

1

−

1

1.19

lim (

x − ln x )

x→0

x2

sin2 x

x→∞

√

1

1.20

lim x e x

1.21

lim

x ln x

1.22

lim tg x · ln x x→0+

x→0+

x→0+

1

1.23

lim tg x · e

x2

1.24

lim x2 e−x2

1.25

lim

x − π

tg x

2

x→0−

x→∞

x→ π +

2

1.26

lim x2 ln x

1.27

lim

x ex

1.28

lim x arctg x

x→0+

x→−∞

x→∞

1.29

lim xx2

1.30

lim

1 + 1 x

1.31

lim (tg x)tg 2x x

x→0+

x→0+

x→0

1

1

1.32

lim

1 sin x

1.33

lim (ln x)

x

1.34

lim

sin x

x2

x

x

x→0+

x→∞

x→0

1

1

1

1.35

lim x

arctg x

(1+x) x − e

x

1.36

lim

x2

1.37

lim

x→∞

x→0

x

x→0

x