Kalkulus – Sifat-Sifat Limit Beserta Contohnya (Bagian 2)

Sifat 5

\[ \lim_{x \rightarrow a}f(x)\times g(x)=\lim_{x \rightarrow a}f(x)\times \lim_{x \rightarrow a}g(x) \]

Contoh

\[ \lim_{x\rightarrow 2}(x^{3}.x^{4}) \]

Jawab

\[ \lim_{x\rightarrow 2}(x^{3}.x^{4})=\lim_{x\rightarrow 2}x^{3}.\lim_{x\rightarrow 2}x^{4} \] \[ \lim_{x\rightarrow 2}(x^{3}.x^{4})=2^{3}.2^{4} \] \[ \lim_{x\rightarrow 2}(x^{3}.x^{4})=8.16 \] \[ \lim_{x\rightarrow 2}(x^{3}.x^{4})=128 \]

Sifat 6

\[ \lim_{x \rightarrow a}\frac{f(x)}{g(x)}=\frac{\lim_{x \rightarrow a}f(x)}{\lim_{x \rightarrow a}g(x)} \]

Contoh

\[ \lim_{x\rightarrow 2}\frac{x^{4}}{x^{3}} \]

Jawab

\[ \lim_{x\rightarrow 2}\frac{x^{4}}{x^{3}}=\frac{\lim_{x\rightarrow 2}2^{4}}{\lim_{x\rightarrow 2}2^{3}} \] \[ \lim_{x\rightarrow 2}\frac{x^{4}}{x^{3}}=\frac{2^{4}}{2^{3}} \] \[ \lim_{x\rightarrow 2}\frac{x^{4}}{x^{3}}=\frac{16}{8} \] \[ \lim_{x\rightarrow 2}\frac{x^{4}}{x^{3}}=2 \]

Sifat 7

\[ \lim_{x \rightarrow a}\left [ f(x) \right ]^{n}=\left [ \lim_{x \rightarrow a}f(x) \right ]^{n} \]

Contoh

\[ \lim_{x\rightarrow 2}(x^{4}+1)^{2} \]

Jawab

\[ \lim_{x\rightarrow 2}(x^{4}+1)^{2}=(\lim_{x\rightarrow 2}(x^{4}+1))^{2} \] \[ \lim_{x\rightarrow 2}(x^{4}+1)^{2}=(2^{4}+1)^{2} \] \[ \lim_{x\rightarrow 2}(x^{4}+1)^{2}=(16+1)^{2} \] \[ \lim_{x\rightarrow 2}(x^{4}+1)^{2}=17^{2} \] \[ \lim_{x\rightarrow 2}(x^{4}+1)^{2}=289 \]

Sifat 8

\[ 8. \lim_{x\rightarrow a}\sqrt[n]{f(x)}=\sqrt[n]{\lim_{x\rightarrow a}f(x)} \]

Contoh

\[ \lim_{x\rightarrow 2}\sqrt[3]{x^{3}} \]

Jawab

\[ \lim_{x\rightarrow 2}\sqrt[3]{x^{3}}=\lim_{x\rightarrow 2}\sqrt[3]{2^{3}} \] \[ \lim_{x\rightarrow 2}\sqrt[3]{x^{3}}=\lim_{x\rightarrow 2}\sqrt[3]{8} \] \[ \lim_{x\rightarrow 2}\sqrt[3]{x^{3}}=2 \]

Materi Lengkap

Berikut adalah beberapa materi lengkap yang membahas tuntas mengenai Limit.


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