What is the limit as x approaches infinity of (3^{x+1})/(4^x) ?

The limit as x approaches infinity of (3^{x+1})/(4^x) is 0

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limit as x approaches infinity of (3^{x+1})/(4^x)

x \to \infty lim (\frac{3 ^{x + 1}}{4 ^{x}})

0

Solution steps

x \to \infty lim (\frac{3 ^{x + 1}}{4 ^{x}})

Simplify

3^{x + 1} : 3^{x} \cdot 3

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

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

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

Apply exponent rule:

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

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

Apply the common limit:

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

= 3 \cdot 0

Simplify

= 0

x \to 2 lim (sin (π x))

x \to 0 + lim (x^{3} e^{- x^{2}})

x \to 3 lim (e^{\frac{1}{x}})

x \to 0 + lim (\frac{x + 1}{2 ^{x} - 1})

x \to 1 - lim (x^{2} - 10 x + 8)

What is the limit as x approaches infinity of (3^{x+1})/(4^x) ?
The limit as x approaches infinity of (3^{x+1})/(4^x) is 0