# Sifat-sifat Limit

## Konsep Dasar

###### SIFAT-SIFAT LIMIT

Jika $$\displaystyle \lim_{x\to c} f(x) = L$$ dan $$\displaystyle \lim_{x\to c} g(x) = M$$

1. Aturan penjumlahan

$$\displaystyle \lim_{x\to c} (f(x) + g(x)) = \lim_{x\to c} f(x) + \lim_{x\to c} g(x) = L + M$$

2. Aturan pengurangan

$$\displaystyle \lim_{x\to c} (f(x) - g(x)) = \lim_{x\to c} f(x) - \lim_{x\to c} g(x) = L - M$$

3. Aturan perkalian konstanta

$$\displaystyle \lim_{x\to c} (k \:.\: f(x)) = k \:.\: \lim_{x\to c} f(x) = k \:.\: L$$

4. Aturan perkalian fungsi

$$\displaystyle \lim_{x\to c} (f(x) \:.\: g(x)) = \lim_{x\to c} f(x) \:.\: \lim_{x\to c} g(x) = L \:.\: M$$

5. Aturan pembagian fungsi

$$\displaystyle \lim_{x\to c} \dfrac {f(x)}{g(x)} = \dfrac {\displaystyle \lim_{x\to c} f(x)}{\displaystyle \lim_{x\to c} g(x)} = \dfrac {L}{M}$$

6. Aturan pangkat

$$\displaystyle \lim_{x\to c} [f(x)]^n = [\lim_{x\to c} f(x)]^n = L^n$$

7. Aturan akar

$$\displaystyle \lim_{x\to c} \sqrt [n] {f(x)} = \sqrt [n] {\lim_{x\to c} f(x)} = \sqrt [n] {L}$$

Jika n bilangan genap dan L bernilai negatif, maka limit tidak ada.