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USM ITT 2010

Solusi USM IT Telkom 2010 Kode 11 – Nomor 21


\lim\limits_{x \rightarrow 4} \frac{sin(\sqrt{x}-2)}{x^2-4x}=....
(A)\quad  \frac{1}{14}
(B)\quad  \frac{1}{15}
(C)\quad \frac{1}{16}
(D)\quad \frac{1}{17}
(E)\quad 17
Jawaban: C

\begin{array} {rcl} \lim\limits_{x \rightarrow 4} \frac{sin(\sqrt{x}-2)}{x^2-4x}&=&\lim\limits_{x \rightarrow 4} \frac{sin(\sqrt{x}-2)}{x(x-4)}\\\\&=&\lim\limits_{x \rightarrow 4} \frac{sin(\sqrt{x}-2)}{x(\sqrt{x}-2)(\sqrt{x}+2)}\\\\&=&\lim\limits_{x \rightarrow 4} \Big[\frac{sin(\sqrt{x}-2)}{\sqrt{x}-2}\times \frac{1}{x}\times \frac{1}{\sqrt{x}+2}\Big]\\\\&=&1\times \frac{1}{4}\times \frac{1}{4}\\\\&=&\frac{1}{16}\end{array}

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