Quiz(69/100)[tex] \: \: [/tex]#zuzah.... Question from @Aikey

ZouYiFeng01

Jawab : B. -1/32

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Cara :

Lim x → 3 1/(x - 3){1/x - 7 - 2/x 11}

Lim x → 3 1/(x - 3){-x + 3/(x - 7)(x - 11)} = Opsi B. -1/32

Nxaa~

3 votes Thanks 4

$\begin{aligned}\lim_{x \to 3} \end{aligned} ( \frac{1}{(x - 3)} ( \frac{1}{x - 7} - \frac{2}{x - 11} )) \\$

$= \begin{aligned}\lim_{x \to 3} \end{aligned} ( \frac{1( \frac{1}{x - 7} - \frac{2}{x - 11} )}{x - 3} ) \\$

$= \begin{aligned}\lim_{x \to 3} \end{aligned} ( \frac{ \frac{d}{dx} (1( \frac{1}{x - 7} - \frac{2}{x - 11} ))}{ \frac{d}{dx} (x - 3}) ) \\$

$= \begin{aligned}\lim_{x \to3 } \end{aligned} ( \frac{ \frac{ {x}^{2} - 6x - 23 }{( {x}^{2} - 18x + 77 {)}^{2} } }{1} ) \\$

$= \begin{aligned}\lim_{x \to 3} \end{aligned} ( \frac{ {x}^{2} - 6x - 23 }{( {x}^{2} - 18x + 77 {)}^{2} } ) \\$

$= \frac{ {3}^{2} - 6 \times 3 - 23 }{( {3}^{2} - 18 \times 3 + 77 {)}^{2} }$

$= \frac{ - 32}{ {32}^{2} }$

$= \frac{ - 1}{32}$

$= - \frac{1}{32}$

2 votes Thanks 1