Kalkulus – Sifat-Sifat Limit Beserta Contohnya (Bagian 1)

Sifat 1

\[ \lim_{x\rightarrow a}c=c \]

Contoh

\[ \lim_{x\rightarrow 2}7 \]

Jawab

\[ \lim_{x\rightarrow 2}7 =7 \]

Sifat 2

\[ \lim_{x\rightarrow a}x^{n}=a^{n} \]

Contoh

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

Jawab

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

Sifat 3

\[ \lim_{x\rightarrow a} cf(x)=c\lim_{x\rightarrow a}f(x) \]

Contoh

\[ \lim_{x\rightarrow 2}4x+8 \]

Jawab

\[ \lim_{x\rightarrow 2}4x+8=\lim_{x\rightarrow 2}4(x+2) \] \[ \lim_{x\rightarrow 2}4x+8=4(\lim_{x\rightarrow 2}(x+2) ) \] \[ \lim_{x\rightarrow 2}4x+8=4(2+2) \] \[ \lim_{x\rightarrow 2}4x+8=16 \]

Sifat 4

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

Contoh

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

Jawab

\[ \lim_{x\rightarrow 2}(x^{3}+x^{4})=\lim_{x\rightarrow 2}x^{3}+\lim_{x\rightarrow 2}x^{4} \] \[ \lim_{x\rightarrow 2}(x^{3}+x^{4})=2^{3}+2^{4} \] \[ \lim_{x\rightarrow 2}(x^{3}+x^{4})=8+16 \] \[ \lim_{x\rightarrow 2}(x^{3}+x^{4})=24 \]

Materi Lengkap

Berikut adalah beberapa materi lengkap yang membahas tuntas mengenai Limit.


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