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Soal 11

Nomor 11

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = ....

$0$

$1$

$10$

$25$

$125$

Pembahasan

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = \lim_{x \to \infty} \left[5^{3x} \left(\frac{1}{5^{2x}} + 1\right)\right]^{\frac{1}{x}}

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = \lim_{x \to \infty} 5^3 \left[\left(\frac{1}{5^{2x}} + 1\right)\right]^{\frac{1}{x}}

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = \lim_{x \to \infty} 5^3 \left[\left(\frac{1}{5^{2x}} + 1\right)\right]^{\frac{1}{x}}

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = 5^3 \left(\frac{1}{\infty} + 1\right)^{\frac{1}{\infty}}

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = 5^3 (0 + 1)^0

\lim_{x \to \infty} (5^x + 5^{3x})^{\frac{1}{x}} = 125

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Soal 11Set 2

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Nomor 11

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