CONTOH 3-LIMIT FUNGSI

 $\begin{aligned}11.\quad&\textrm{Perhatikan gambar grafik fungsi}\:\: y=f(x)\: \: \textrm{berikut}\end{aligned}$.

$\begin{aligned}\quad\qquad&\textrm{Jika}\:\: a\in \left\{ 0,2,4 \right\}\:\: \textrm{dengan}\:\: \underset{x\rightarrow a }{\textrm{Lim}}\: f(x)\:\: \textrm{ada, maka}\\ &\textrm{untuk nilai semua}\:\: a\:\: \textrm{yang memenuhi adalah}\: ....\\ &\textrm{a}.\quad a=0\\ &\textrm{b}.\quad a=2\\ &\textrm{c}.\quad a=0\:\: \textrm{dan}\:\: a=2\\ &\textrm{d}.\quad a=0\:\: \textrm{dan}\:\: a=4\\ &\textrm{e}.\quad a=0\:,\: a=2\:,\: \textrm{dan}\:\: a=4\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Cukup jelas sesuai ilustrasi gambar, bahwa}\\ &\bullet \quad\underset{\displaystyle x\rightarrow  0^{\displaystyle  -} }{\textrm{Lim}\qquad}\: f(x)=\underset{\displaystyle x\rightarrow  0^{\displaystyle  +} }{\textrm{Lim}\qquad}\: f(x)=6\\ &\textrm{dan}\\ &\bullet \quad \underset{\displaystyle x\rightarrow  2^{\displaystyle  -} }{\textrm{Lim}\qquad}\: f(x)=\underset{\displaystyle x\rightarrow  2^{\displaystyle  +} }{\textrm{Lim}\qquad}\: f(x)=2\\ &\textrm{serta nilai}\\ &\bullet \quad \underset{\displaystyle x\rightarrow  4^{\displaystyle  -} }{\textrm{Lim}\qquad}\: f(x)\neq \underset{\displaystyle x\rightarrow  4^{\displaystyle  +} }{\textrm{Lim}\qquad}\: f(x)  \end{aligned}$.