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SMK Teknologi dan Rekayasa

Solusi Paket 59 UN 2011 Matematika SMK Teknologi (40)


\lim\limits_{x\rightarrow -3} \frac{2x^2+5x-3}{x^2+x-6}= ....\\\\A.\ \ 0\ \ \ \ \ \ \ \ \ \ B.\ \ \frac{7}{5}\ \ \ \ \ \ \ \ \ \ C.\ \ \frac{17}{7}\ \ \ \ \ \ \ \ \ \ D.\ \ 3\ \ \ \ \ \ \ \ \ \ E.\ \ 5
Jawaban: B
Alternatif 1, dengan menggunakan faktorisasi
\begin{array}{rcl}\lim\limits_{x\rightarrow -3} \frac{2x^2+5x-3}{x^2+x-6}&=&\lim\limits_{x\rightarrow -3} \frac{(2x-1)(x+3)}{(x-2)(x+3)}\\\\&=&\lim\limits_{x\ \rightarrow \ -3} \frac{2x-1}{x-2}\\\\&=&\frac{2(-3)-1}{-3-2}\\\\&=&\frac{-6-1}{-5}\\\\&=&\frac{-7}{-5}\\\\&=&\frac{7}{5}\end{array}
Alternatif 2, dengan menggunakan turunan/diferensial (Dalil L’Hospital)
\begin{array}{rcl}\lim\limits_{x\rightarrow -3} \frac{2x^2+5x-3}{x^2+x-6}&=&\lim\limits_{x\rightarrow -3} \frac{2(2)x+5-0}{2x+1-0}\\\\&=&\lim\limits_{x\rightarrow -3} \frac{4x+5}{2x+1}\\\\&=&\frac{4(-3)+5}{2(-3)+1}\\\\&=&\frac{-12+5}{-6+1}\\\\&=&\frac{-7}{-5}\\\\&=&\frac{7}{5}\end{array}

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2 thoughts on “Solusi Paket 59 UN 2011 Matematika SMK Teknologi (40)

  1. Semangat ngeblog matematika🙂

    Posted by zholieh | 15 November 2011, 8:36 AM

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