Limit Fungsi Soal Jawab

8/8/2019 Limit Fungsi Soal Jawab

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Soal Latihan dan PembahasanLimit FungsiDi susun Oleh :Yuyun Somantri1http://bimbinganbelajar.net/Di dukung oleh :Portal edukasi Gratis Indonesia

Open Knowledge and Educationhttp://oke.or.idTutorial ini diperbolehkan untuk di copy, di sebarluaskan, di print dan diperbaiki dengan tetapmenyertakan nama penulis.tanpa ada tujuan komersial1 Lahir di Bandung tahun 1956, Lulus dari SMK Kimia melanjutkan studinya ke UPI(IKIP Bandung), lalumeneruskan studinya lagi bidang matematika dan dari tahun 1984 sampai saat ini mengajar matematika diSMA Negeri 3 Tasikmalaya


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1

Limit Fungsi

limx2- 4

1. = .....x 2x3+ 1

Jawab :

limx2- 44- 4

3== 0

x 2x

+ 18+ 1

limx2+ 3x- 18

2. 2= ....x 3x- 3x

Jawab :

lim(x+ 6)(x- 3)3+ 6

== 3


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x 3x(x- 3)3

lim

t- 23. = ....t 4t- 4

Jawab :

limt- 211

==t 4(

t- 2)(t+ 2)2+ 24

lim9- x2

= ....

4.x 3

4-

x2+ 7Jawab :

lim16


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- (x2+ 7)lim(4-

x2+ 7)(4+

x2+ 7)== 4+ 4= 8

x 3

2x

34-

x+ 74-

x2+ 7limx2- 4

5. = .....x x3+ 1

Jawab :

limx2lim1

== 0

x x3x x


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11.12.13.14.15.3

limsin(x- 2)

= .......

x

2x2- 4

Jawab :

limsin(x- 2)limsin(

x- 2)111

= .= 1.=

x 2(x- 2)(x+ 2)x 2x- 2x+ 22+ 24

limx2+ x- 6

= ......


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x 3x2+ 5x+ 6

Jawab :

limx2+ x- 69+ 3- 61

==

x 3x2+ 5x+ 69+ 15+ 65

lim2x2- x- 1

= ......

x 13x2- x- 2

Jawab :

lim4x- 13

= (Menggunakan bantuan turunan)

x 16x- 15

lim

1- x2


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= ......

x 1x- 1

Jawab :

lim- 2x

=- 2

x

11

lim2x2- 2

= ......

x 1

x- 1

Jawab :

lim4x

= 4

x 11


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416. = ......limt3- 8t

2t2+ t- 6Jawab :t 22t+ 1lim3t2=

51217. = ......lim(3x- 1)2- 4x 1x2+ 4x- 5Jawab :

lim18x- 6=x 12x+ 4612= 2lim 2x2- 8x2- 2x 18. + = ......x 2x- 22x

- 4Jawab :lim


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(x- 2)(2x+ 4) +x 2x

- 22(x-x(x-2)2) = 4+ 4+22= 919. - = ......

lim 6- x1x 2 x2- 4x- 2Jawab :lim- 2(x

- 2)x 2(x- 2)(x+ 2)=4- 2= -2120. 2= .....lim6x2- 4xx 02x+ xJawab :lim12

x- 4x


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04x+ 1=1- 4= - 4


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limx- 1

21. =x

11-

Jawab :

limx 1

limx2- 16

22. =x 4

x- 4Jawab :

limx

4

lim3-

2x+23......

x 0x

Jawab :

lim3-

2x

+ 93+2x+ 9


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lim9- 2x- 9- 21.= ==-

x 0x3+

2x+ 9x 0x(3+2x+ 9)

3+ 33limx2- 9

24. = ......x 3

x2+ 16

Jawab :

limx 3

lim

x- x25. =x 0

x+ x

Jawab :

lim

x 0


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.......

11

=- =- 2

- 11

2

2

x

......

(

x- 4)2(x+ 4)lim

=

x- 4(x+ 4)= 0.8= 0x- 4x 49

=

- 5

(

x2

+ 16- 5)(x2


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+ 16+ 5)= 5+ 5= 10

x2

+ 16- 5.......

x(1-x)1- 0== 1

x)1+ 0x(1+


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26.27.28.29.30.6

lim

6x- 2-3x+ 7= ......

x 3x- 3

Jawab :

lim

6x- 2- 3x+ 76x- 2+ 3x+ 7.

x 3x- 3

6x- 2+ 3x+ 7lim3(x- 3)3

==x 3(x


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- 3)(6x- 2+ 3x+ 7)8

lim2x2- 5x

= ......x 03- 9+ x

Jawab :

lim2x2- 5x3+ 9+ xx(2x- 5)(3+ 9+ x)- 5(3+ 3)

.= == 30x 03- 9+ x

3+ 9+ x- x- 1

lim

x2+ 3- x- 1= .......

x 11- x2

Jawab :

lim

x2

+ 3- (x+ 1)


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x2+ 3+ (x+ 1)lim2(1- x)1.

==

x 11- x2

x2+ 3+ (x+ 1)x 1

(1- x)(1+ x)(x2+ 3+ x+ 1)4323

lim

x

- 2x+ 1= ......

x 1(x- 1)2

Jawab :

lim(3x- 1)211

==

33232

x 1(


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x+ 1)(1+ 1+ 1)29x

- 1)(x+

limx- 27

= ......

x 273x- 3

Jawab :

3323

lim

(

x- 3)(x+ 3x+ 9)= 9+ 9+ 9= 27

x 273x- 3


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7

lima

a- bb31. = .......a b

a- bJawab :

lim(

a-b)(a+ab+ b)= b

+

b.b+ b= 3ba b

a- blimax+ b-

x332.Jika = maka tentukan a + bx 4x- 44

Jawab :


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0

Bentuk di atas jika x = 4 maka harus berbentuk .

0

Jadi4a+b2=0 atau4a+b=2 ..(1)Dengan menggunakan bantuan turunan maka :

- 1

lima2

x313= a-= a= 1x 41444

4.1+ b= 2

b=- 2a+ b= 1- 2=- 1lim(2x- 3x+ 1)(

x- 1)

33. 2= .......x 1(x- 1)

Jawab :

lim(


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x- 1)2(2x- 1)2- 11

==

x 1(

x+ 1)(1+ 1)24x

- 1)2(lim1+ x- 1

34. = ......x 031+ x- 1

Jawab :

lim6626

(1+ x- 1)((1+ x)+ 1+ x+ 1)1+ 1+ 13

==x 0(61+ x- 1)(61+ x+ 1)1+ 12


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35.36.37.38.39.8

lim

2+

x-2-

x

= ........

x 0

x

Jawab :

lim

2+

x-2-

x

2+

x

+


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2-

x

.

x 0

x

2+

x+

2-

x

lim

2

x21= ==

2

x 0

222+x(2+x+

2-

x


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)lim 23

-= .......

22

x 2 x- 4x+ 2x- 8

Jawab :lim2(x+ 4)- 3(x+ 2)lim- (x- 2)1

= =-

x 2(x- 2)(x+ 2)(x+ 4)x 2(x- 2)(x+ 2)(x+ 4)24

lim

(2x- 5)(2x+ 1)- (2x

- 5)= .......x


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Jawab :

lim

- 8- (- 20)

4x2- 8x- 5-

4x2- 20x

+ 25== 3

x

24

lim2x2

+ 3x

= ......

x

x2- xJawab :

lim2x2lim

= 2x=

x

2x


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x

lim

x(4x+ 5)-

4x2+ 3= .......

x

5

Jawab :

lim

25- 054x2+ 5x

-

4x+ 0x+ 3==

x 5

244


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9

lim

(x+ a)(x+ b)- x= .......40.x

Jawab :

lim

2a+ b- 0a+ bx2+ (a

+ b)x+ ab-x+ 0x==

x

212

limcos2x

41. p= .........x 4sinx- cosx

Jawab :


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2+ 122

lim(cos

x- sinx)(cosx+ sinx)12

p ==-

2

x 4- (cosx- sinx)- 1

lim

sinax

42. = .......x 0sinbx

Jawab :

limsinaxbxalimsinaxbxaaa

..= ..


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= 1.1.=

x 0sinbx

axbx 0axsinbxbbb

lim

sin2x43. = .......x 03-

2x+ 9Jawab :

lim2sinxcos

x3+

2x+ 9.

x 03-

2x+ 93+2x+ 9limsinxcosx.(3+

2x+ 9)1.(3+ 3)= .

= 1.=- 6


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x 0x- 1- 1

lim1- cosx

44. = ........x 0xsin2x

Jawab :

21111

lim2sinxlimsinxsinx1

2222

= .= 1.=

x 0xsin2xx 012xsin2x24


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45.46.47.48.49.10

limxtanx

= ........

x

01- cos2x

Jawab :

limxtanxlim1xtan

x1

= ..=

x 02sin2xx 02sinxsinx2

limtanx

= .......


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x 0x2+ 2x

Jawab :

limtanx111

.= 1.=

x 0xx+ 222

lim1- cosx

= ......

x 05x2

Jawab :

lim2sin212x2111

= ..=

x 05x252210

lim


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sinx

= ......x 01- x

- 1

Jawab :

limsinx1- x+ 1limsin

x1- x+ 11+ 1

.= .= 1.=- 2x 01- x- 11- x+ 1

x 0x- 1- 1

limcotx

= ......

x 0cot2x

Jawab :

lim1lim

tan2x

tan


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x

== 2

x

01x 0tanx

tan2x


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50.51.52.53.54.11

limsin4x+ sin2x

= ......

x 03xcos

x

Jawab :

lim2sin3xcosx

= 2.1= 2

x 03xcosx

limxsinx

= .......

x 01- cos4x

Jawab :

limxsinxlim1x

sinx111


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1

= ..= ..=

x 02sin22xx 02sin2xsin2x2228

lim

cos4x- 1

= .......

x 0xtan2x

Jawab :

lim- 2sin22xlimsin2xsin2x22

=- 2..=- 2..=- 4

x 0xtan2xx 0xtan2x

12


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limsin22x

= ........

x 0x2cos2x

Jawab :

limsin2xsin2x1

221

..= ..= 4

x 0xxcos2x111

lim7x2+ sin(2x2)

= ........

x 0tan23x

Jawab :

lim(7x)2sin(2x)272

=+= 1


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x 0(tan3x)2+(tan3x)299


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55.56.57.58.59.12

........cos3cos51cos40lim=-- xxxxJawab :

2sin4sin2sin20lim2-- xxxx=

0limxsinsin2.sin4sin2xxxx=12.42= 1........sin340lim=

+ xxxx


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Jawab :10lim4sin3

= +xxxx0limx14sin34

1+ xx= 141+ 43= 1........sin3)sin(2

0lim222=+ xxxxJawab :10limsin(2)sin3sin22222+x

xxxx


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= 121+ 29=5

1...........sin3.cos226sin4.tan30lim232= +

xxxxxxxJawab :7.131.13.1.29.3

4cos21.(2)tan3.sin3sin40lim22=+=+ xxxxxxcos21

.sin3..


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2622xxxx

x........cossincos10lim422= -- x

xxxxJawab :sin.sin2.0limcos)(1sin0lim2

2212242= - xxxxxxxxx= 2.1.()2212=21


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13

limsin(1- 1x

)cos(1- 1x)

60. = ........x 1x- 1

Jawab :

1111

limsin(1- x)cos(1- x)limsin(1- x)cos(1- x)

= .= 1.1= 1x 1x(1- 1x)x 11- 1xx

limsin(p x-p )

61. = ........x 1(x- 1)cos(p x-p )

Jawab :

limsin


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p (x- 1)1

.=p .1=p

x 1x- 1cos(p x-p )

limx- k

62. = ........x ksin(x- k)+ 2k- 2x

Jawab :

lim1

1

=

sin(x- k)2(x- k)=- 1

x k- 1- 2

x- kx- k

lim1- cos2(x- 2)

63. = ........x


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23x2- 12x+ 12

Jawab :

limsin2(x- 2)limsin(x- 2)sin(x- 2)1

1

= ..=

x 2(x- 2)(3x- 6)x 2x

- 2x- 233

lim(x+ 6)sin(x+ 2)

64. 2= .......x- 2x- 3x- 10

Jawab :

limx+ 6

sin(x+ 2)4


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.=-

x- 2

x- 5x+ 27

limx2sin2x

65. = .......xp x

-pJawab :

lim2xsin2x+ 2x2cos2x22

= 0+ 2p= 2p

xp 1


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Limit Fungsi Soal Jawab

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