MATEMATICA, ENSINO MÉDIO LIMITES - … Resolvidos, Limites 2.pdfPage | 1 MATEMATICA, ENSINO MÉDIO...

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Page | 1 MATEMATICA, ENSINO MÉDIO LIMITES - EXERCICIOS RESOLVIDOS. MATEMÁTICA Exercícios Resolvidos De Limites 1. 4 1 ) 1 cos 1 )( 1 cos 1 ( 1 ) cos 1 )( cos 1 ( ) cos 1 )( cos 1 ( ) cos 1 )( cos 1 ( ) cos 1 ( cos 1 ) cos 1 ( ) cos 1 ( ) cos 1 )( cos 1 ( cos 1 2 2 2 2 2 0 2 2 2 2 0 2 0 ) cos 1 ( x n x n x x x x x x x se x x x se x x x x Lim x x x x x x Lim x Lim x x x 2. 2 1 ) cos 1 ( ) cos 1 ( ) cos 1 )( cos 1 ( cos 1 0 0 cos 1 2 2 2 2 0 0 x x se x x x x Lim x x Lim x n x x x x 3. 2 2 4 cos cos cos cos ) (cos cos cos cos cos 1 cos 0 0 1 cos 4 4 4 x x x Lim x senx x x senx x x senx x x senx x senx x senx Lim tgx x senx Lim 4. 2 0 1 2 1 2 3 2 3 2 3 3 3 3 x x x x x x x x x Lim x x x Lim x x 5.

Transcript of MATEMATICA, ENSINO MÉDIO LIMITES - … Resolvidos, Limites 2.pdfPage | 1 MATEMATICA, ENSINO MÉDIO...

Page | 1

MATEMATICA, ENSINO MÉDIO

LIMITES - EXERCICIOS RESOLVIDOS.

MATEMÁTICA

Exercícios Resolvidos De Limites

1.

4

1

)1cos1)(1cos1(

1

)cos1)(cos1()cos1)(cos1(

)cos1)(cos1(

)cos1(

cos1

)cos1()cos1(

)cos1)(cos1(cos1

2

2

2

2

20

22

2

2020

)cos1(

x

n

x

n

x

xx

x

xxxse

xx

xse

xx

xxLim

x

x

xx

xxLim

xLim

x

xx

2.

2

1

)cos1()cos1(

)cos1)(cos1(cos1

0

0cos12

2

2200

x

xse

x

xxxLim

x

xLim

x

n

xxxx

3.

2

2

4cos

coscos

cos)(cos

cos

cos

cos

cos1

cos

0

0

1

cos

4

44

x

xx

Lim

xsenxx

xsenxx

x

senxx

xsenx

x

senx

xsenxLim

tgx

xsenxLim

4.

201

2

1

2

32

32

3 3

33

x

x

x

x

x

x

xx

x

Limxx

xLim

xx

5.

Page | 2

21

2

2

1

)1)(2(

)1)(1(

0

0

23

1

12

2

1

x

x

xx

xxLim

xLim

xx x

x

6.

12

12

)11(

11

)11(

)11(

)11()11(

0

011

)1()1(22

00

x

x

xxx

xx

xxx

xxx

xxxxLim

x

xxLim

xx

xx

7. 2

2

x

SenxLimX

8. 2

3

2

3

0

xSen

xSenLimX

9. 2

1

1

1

)1(0

012

2

2

2

20

Cosx

xSe

Cosx

xSeCosxLim

x

n

x

n

xX

10. 4

1

)cos1)(cos1()cos1(

1

)cos1(

1

0

012

2

22

2

20

)cos(

xx

xse

x

Cosx

x

CosxLim

x

n

xx

x

xX

11. 5

5

0

x

xTgLimX

12. 2

1

)cos1()cos1(

)cos1)(cos1(cos1

0

0cos12

2

220

x

xse

x

xxx

x

xLim

x

n

xxX

Page | 3

13.

x

senxsenxLimx

11

0 = 0

0

↔ )11(

)11)(11(

0senxsenxx

senxsenxsenxsenxLimx

)11(

)1()1(22

0senxsenxx

Limsenxsenx

x

= )11(

12

senxsenxx

senx

= 1

14.

0

0

cos

37

0

xx

xsenxsenLimx

40cos

14

cos

14

cos

4

0

xx

xsen

xx

xsenLimx

15.

0

0

cos10

x

senxtgxLimx x

senxx

senx

Limx cos1

cos0

= x

x

xsenx

cos1

cos

)cos1(

=

)cos1(cos

)cos1(

xx

xsenx

00

tgxLimx

16. 2

2

cos

cos

cos

cos1

cos

0

0

14

x

senxx

xsenx

x

senx

xsenx

tgx

CosxSenxLimX

17. 4

1

31

21

3

2

3

2

0

x

xsen

x

xx

xsen

x

x

xsenx

xsenxLimX

Page | 4

18.

e

x

senx

xsenx

xsenxLimLim

e

esenxX

XsenxLim

X

X

X

1

0

1)11(

1

01

11)11(01)1(

19.

exxse

xse

xse

x

xsexLimnnLim

en

n

nnex

XXSe

xLimXSe

X

X

2

1

2

2

220

1)cos2(

1

0

2

1

)cos1(

cos11)1cos2(20

2

1)cos2(

20.

ee

ex

x

x

x

xx

xxx

x

xLimLimX

XX

XLim

X

X

X

4

4

)2(3

1

2

14

3

)2(4

)2(3

31)2(1

3

11

3

1

21. 1

3

2

03

02

3

200

0

x

xX

XLim

22. 02

1 1

2

x

X

X

XLim

23. eeaxab

X

baXLim

X

b

X x

abx

x

baxLim X

1111

0

011

24.

0

1

1

6

3

6

3

6

3

6

3

6

6

3

36n

n

n

n

n

n

n

n

Xn

nn

nLimLim

Page | 5

25.

66

2

3

33

3

3

3

33

3 2

3

3

2

3

2n

n

n

n

n

n

n

n

n

n

n

n

nLim

n

nn

26. 4

5

16

25

162

255

162

255

n

n

n

n

n

n

n

nLimn

27.

ee

en

n

Logo

n

n

n

nn

n

nnLim

nn

nLim

n

n

n

4

4

12112

32

12

1:

42

8

12

12412

12

12321

12

32

28.

2

3

11

3

23

23

23

23

23

2323

23

2

22

22

2

n

nn

nn

n

n

n

nn

nnnn

nnLim

n

nn

nnn

n

29.

4

1

1

1

1

4444

44

4

2

4

3

4

3

44

42

44

44

4

3

4

3

44

44

244

3344

24

34

132

3

2

3

2

3

2

3

2

3

3

3

2

3

2

3

22

3

22

n

n

n

n

n

n

n

n

n

n

nn

nn

nn

nn

nLim

Page | 6

30.

21

2

21

11

0

0

23

12

2

1

xx

xx

xLim

xx

X

31.

aaxaxaxx a

ax

x

axax

xaxaxaLim

aX2222233

2

3

111

0

01

32.

03

0

1

2

21

22

0

0

23

42

2

2

x

x

xx

xx

xLim

xx

X

33.

2

1

11

1

11

1

11

11

0

0

1

1

2

1

xx

x

xxxx

xx

x

xLim

xX

34.

2

3

13

0

0

3

342

3

x

xx

x

xLim xX

35.

2

1

1

11

0

012

2

1

x

x

xx

xx

xLim

xx

X

36.

328442

2

422

2

44

2

2

0

0

2

16 2

222224

2

4

x

xxxxx xx

xx

xxxLimX

37.

3

2

42

22

22

4

8:

.26464;:log;623;0

0

4

8

222

22

33

36

6

2

66

364

2

2

2

y

y

ýy

yy

Limnovo

yxxoyxx

xLim

yy

y

y

y

y

y

Y

X

Page | 7

38.

2

3

11

11

1

1

1

1:

111623;1;1;00

0

11

11

2

2

3

36

6

1

66

30

yy

yy

Limnovo

yyyxxx

xLim

y

y

y

y

y

y

Y

X

39.

1ln:log;1

lnln1

ln)(ln1ln

11

11

111

eoXx

xx

Limx

xxLimxxxLim

eee

x

x

x

x

Xx

LimXX

XLim

X

X

X

XX

XX

Teória e Pratica:

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Definição de Limite.

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