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

The limit as x approaches infinity of (3^{x+4})/(8^x) is 0

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

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

0

Solution steps

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

Simplify

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}})

Simplify

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

Apply exponent rule:

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

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

Apply the common limit:

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

= 81 \cdot 0

Simplify

= 0

\frac{d}{d x} (\frac{x ^{4} + y ^{4}}{x y})

f (x) = - 3 x^{2} - 2 x, at x = 2

n = 0 \sum \infty (\frac{4}{10})^{n}

\int_{2}^{3} 21 t^{2} d t

n = 1 \sum \infty \frac{n ^{4} x ^{3 n}}{5 ^{3 n}}

What is the limit as x approaches infinity of (3^{x+4})/(8^x) ?
The limit as x approaches infinity of (3^{x+4})/(8^x) is 0