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[tex] \sf \lim\limits_{x \to 3} \dfrac{ {x}^{2} - 9 }{ \sqrt{ {x}^{2} + 16} - 5} [/tex]
[tex]\begin{aligned}\sf &=\sf \dfrac{ {x}^{2} - 9 }{ \sqrt{ {x}^{2} + 16} - 5} \times \frac{ \sqrt{ {x}^{2} + 16} + 5}{ \sqrt{ {x}^{2} + 16} + 5} \\ \sf &=\sf \frac{( {x}^{2} - 9)( \sqrt{ {x}^{2} + 16} + 5)}{ {x}^{2} + 16 - 25 } \\ \sf &= \sf \frac{( \cancel{{x}^{2} - 9})( \sqrt{ {x}^{2} + 16} + 5)}{ \cancel{{x}^{2} - 9 }} \\ \sf &=\sf \lim\limits_{x \to 3} \sqrt{ {x}^{2} + 16 } + 5\\ \sf &=\sf \sqrt{ {3}^{2} + 16} + 5\\ \sf &=\sf \sqrt{9 + 16} + 5\\ \sf &=\sf \sqrt{25} + 5\\ \sf &=\sf 5 + 5 \\ \sf &=\sf 10\end{aligned}[/tex]
Penjelasan dengan langkah-langkah:
lim x² - 9/√x² + 16 - 5
x→3
Lim ( x² - 9/√x² + 16 - 5 ) ( √x² + 16 + 5/√x² + 16 + 5 )
x→3
Lim (x² - 9) (√x² + 16 + 5) / x² + 16 - 25
x→ 3
Lim (x² - 9)(√x² + 16 + 5)/x² - 9
x→3
Lim (√x² + 16 + 5)
x→3
√3² + 16 + 5
√9 + 16 + 5
√25 + 5
5 + 5
10
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