tugas kelompok 1 mtk tentang limit hal : 1-8jawaban mtk

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Materi limit Question Latihan 1 1. F(x)= x+ 2 x5 a. X=3,001 b. X=2,99 c. Observation? 2. F(=x)= x5 4 x a. x=1,002 b. x=0,993 c. observation? 3. f(x)= 3 x 2 x a. x=.001 b. x= -.001 c. observation? Answer : Latihan 1 1. F(x)= x+ 2 x5 a. X=3,001 maka f(x)= 3,001+ 2 3,0015 = 5,001 1,999 = -2,5017 b. X=2,99 maka f(x)= 2,99 +2 2,995 = 4,99 2,01 Politeknik Manufaktur Negeri Bangka Belitung 1

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Page 1: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

Question

Latihan 1

1. F(x)=x+2x−5

a. X=3,001b. X=2,99c. Observation?

2. F(=x)= x−54 x

a. x=1,002b. x=0,993c. observation?

3. f(x)=3x2

xa. x=.001b. x= -.001c. observation?

Answer :

Latihan 1

1. F(x)=x+2x−5

a. X=3,001

maka f(x)=3,001+23,001−5

=5,001

−1,999 = -2,5017

b. X=2,99

maka f(x)=2,99+22,99−5

=4,99

−2,01 =-2,482

Observation It appears that when x is close to 3 in value, then f(x) is close to -2 in value.

1

Page 2: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

2. F(=x)= x−54 x

a. x=1,002

maka f(x)=1,002−54 (1,002)

=-−3,9984,008

=0,9975b. 0,993

maka f(x)=0,993−54 (0,993)

=−4,0073,972

=1,008

Observation: It appears that when x is close to 1 in value, then f(x) is close to 1 in value.

3. f(x)=3x2

xa. x=.0,001

maka f(x)= 3(0.001)2

0,001

=0,0000030,001

=0.0015b. x= -0,001

maka f(x)= 3(−0,001)2

−0,001

=0,000003−0,001

=-0,0015 observation: It appears that when x is close to 0 in value, f(x) is not close to

any fixed number in value.

2

Page 3: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

Question

Latihan 1.2

1.limX→3

x2−4

x+1=

2.limX→2

x2−9

x−2

3. limX→1

√ x3+7 =

4. limX→π

¿(5x2+9) =

5.limX→0

5−3 x

x+11 =

6.limX→0

9+3 x2

x3+11 =

7. limX→1

x2−2x+1

x2−1 =

8.limX→0

6−3 x

x2−16 =

9. limX→−2

√4 x3+11 =

3

Page 4: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

10. .limX→1

8−3 x

x−6=

Answer :1. lim

x→3

x2−4x+1

=limx→3

x2−4

limx→3

x+1=54

2. limx→2

x2−9x−2

=limx→2

x2−9

limx→2

x−2=−5

3. limx→1

¿√x3+7=2√24. limx→π

(5 x2+9 )=¿585. lim

x→0

5−3 xx+11

=limx→05−3 x

limx→0

x+11= 511

6. limx→0

9−3 x2

x3+11=limx→0

9−3 x2

limx→0

x3+11= 911

7. limx→1

x2−2 x+1x2−1

=limx→1

x2−2x+1

limx→1

x3+11=12

8. limx→4

6−3 xx2−16

=limx→46−3 x

limx→4

x2−16= 6−3 x

(x−4)(x+4)

9. limx→−2

√4 x3+11=√4(−8)+11=√−21

4

Page 5: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

10. limx→-6

8−3 xx−6

=limx→-6

8−3x

limx→-6

x−6= 26

−12

Latihan 2.1

1.limX→3

x−3

x2+x−12=

2. limh→o¿¿=

3.limX→4

x3−64

x2−16=

4. IF F(x)=5(x+b), find limX→ 4¿

5.limX→−3

5x+7

x2−3=

5

Page 6: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

6.limX→25

√x−5x−25

= . limX→25

(√ x−5)

(√ x−5)(√ x+5)

7. IF g ( x )= x2 , FindlimX→2

g ( x )−9 (2 )

x−2=¿

8. limX→ 0¿ 2x

2−4 xx

=

9.limr →0

√ x+r−√xr

=

10.limx→4

x3+6

x−4=

Answer

Latihan 2.1

1.limX→3

x−3

x2+x−12=limX→3

x−3

( x−3 ) ( x+4 )

= limX→3

1

x+4

6

Page 7: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

=13+4

=17

2. limh→o¿¿=

limh→o

−x3−xh4

h

=limh→o

¿-xh3

=-x.03

=0

3.limX→4

x3−64

x2−16=limX→4

x3−64

x2−16= limX→4

( x−4 ) (x2+16 )−(16 x+4 x2 )

(x−4 ) ( x+4 )

=limX→4

(x2+16 )−(16 x+4 x2)

(x+4)

=(42+16 )−¿¿

=(16+16 )−(64−64 )

8

=32−1288

= -968

= -12

4. IF F(x)=5(x+b), find limh→0

f (x+h )−f (x)

h

find limh→0

f (x+h )−f (x)

h= find

limh→0

(5 ( x+h )+8)−(5 x+8)

h

7

Page 8: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

=limh→0

5 x+5h+8−5x−8

h

=limh→0

5h

h

=limh→ 0

5

=5

5.limX→−3

5x+7

x2−3=5(−3)+7(−3)2−3

=−15+79−3

=−86

=−43

6.limX→25

√ x−5x−25

= . limX→25

(√ x−5)

(√ x−5)(√ x+5)

= limX→25

1

(√ x+5)

=1

(√25+5)

=1

(5+5)

=110

7. IF g ( x )= x2 , FindlimX→2

g ( x )−9 (2 )

x−2

limX→2

g ( x )−9 (2 )

x−2 = limX→2

2x2−(2)2

x−2

= limX→2

x2−4

x−2

=limX→2

(x−2)(x+2)

(x−2)

8

Page 9: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

=limX→ 2

¿(x+2)

= 4

8. limX→ 0

¿ 2x2−4 xx

= limX→ 0

¿2x-4

= 2.0 – 4= -4

9.limr →0

√ x+r−√ xr

= limr →0

√ x+r−√xr

× √ x+r+√x√ x+r+√x

limr→0

( x+r )−x

r (√ x+r+√x )

limr→0

r

r (√ x+r+√x )

limr→0

1

√x+r+√x

1

√x+0+√x

1

√x+√ x

1

2√x

9

Page 10: Tugas Kelompok 1 MTK Tentang Limit hal : 1-8Jawaban mtk

Materi limit

10.limx→4

x3+6

x−4= 4

3+64−4

=640

= ∞

10