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人気のある微分積分 >

limit as x approaches infinity of (3^{x+4})/(8^x)

解

x \to \infty lim (\frac{3 ^{x + 4}}{8 ^{x}})

解

0

解答ステップ

x \to \infty lim (\frac{3 ^{x + 4}}{8 ^{x}})

簡素化

3^{x + 4} : 3^{x} \cdot 3^{4}

= x \to \infty lim (\frac{3 ^{x} \cdot 3 ^{4}}{8 ^{x}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3^{4} \cdot x \to \infty lim (\frac{3 ^{x}}{8 ^{x}})

簡素化

= 81 \cdot x \to \infty lim (\frac{3 ^{x}}{8 ^{x}})

指数の規則を適用する:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= 81 \cdot x \to \infty lim ((\frac{3}{8})^{x})

共通限度を適用する:

x \to \infty lim (a^{x}) = 0, 0 < a < 1

= 81 \cdot 0

簡素化

= 0

グラフ

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