KALDIF 2.6 TEOREMA LIMIT UTAMA

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Kalkulus Differensial – Nur Insani 2012

1 [email protected]

2.6. TEOREMA LIMIT UTAMA

Andaikan bil. bulat positif, konstanta, &

fungsi-fungsi yg mempunyai limit di �. Maka:

1. �

→ � = 2. �

→ � = 3. �

→ � = �→ � 4. �

→ � ± = �→ � ± �→ � 5. �

→ � . = �→ � . �→ �

6. �

→ �

=

�

→�

�

→�

, asal �

→ � ≠ 0

7. �

→ � = �→ � 8. �

→ � = �→ � , asal �

→ � > 0 jk n genap.

Contoh:

1. �

→ −13

2 − _{1 =} �

→ −13

2 − �

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2 [email protected]

= 3 �

→ −1

2 − _{1 = 3} �

→ −1

2

− 1

= 3 −1 2 − 1 = 2

2. �

→ −2

3 _{+ 6}

4

= �

→ −2

3 _{+ 6}

4

= �

→ −2

3 ₊ �

→ −26

4

= 4 −8 − 12

= 4 −20 (tidak ada).

∴ �_{→ �} harus > 0 jk n genap (sifat 8).

Teorema Substitusi

Jika suatu fungsi polinom atau fungsi rasional, maka

�

→ � = �

asalkan dlm kasus fs. rasional, penyebut ≠ 0.

Contoh:

1. � → 1

3 _{+ 2} 2 ₊ _{+ 6}

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3 [email protected]

Soal Tambahan

1. � → 0

5 3+8 2

3 4−16 2

2. � → 1

3₋₁

−1

3. � → 4

−4

−2

4. � → 2

1

−2 −

4

2₋₄

5. �

→ 0−

6. �