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SMK Teknologi dan Rekayasa

Indikator UN 2011 Matematika SMK Teknologi (32)


Indikator 32
Menentukan nilai limit fungsi aljabar

\lim\limits_{x \rightarrow 2} \frac{3x^2-4x-4}{x^2-4}= ....
a.\ \ 0\\b.\ \ 1\\c.\ \ 2\\d.\ \ 3\\e.\ \ \infty
Jawaban: c
Alternatif 1, dengan menggunakan faktorisasi
\begin{array}{rcl}\lim\limits_{x \rightarrow 2} \frac{3x^2-4x-4}{x^2-4}&=&\lim\limits_{x \rightarrow 2} \frac{(3x+2)(x-2)}{(x-2)(x+2)}\\\\&=&\lim\limits_{x \rightarrow 2} \frac{3x+2}{x+2}\\\\&=&\frac{3(2)+2}{2+2}\\\\&=&\frac{8}{4}\\\\&=&2\end{array}

Alternatif 2, dengan menggunakan turunan/diferensial (Dalil L’Hospital)
\begin{array}{rcl}\lim\limits_{x \rightarrow 2} \frac{3x^2-4x-4}{x^2-4}&=&\lim\limits_{x \rightarrow 2} \frac{3(2)x-4-0}{2x-0}\\\\&=&\lim\limits_{x \rightarrow 2} \frac{6x-4}{2x}\\\\&=&\frac{6(2)-4}{2(2)}\\\\&=&\frac{8}{4}\\\\&=&2\end{array}

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