What is the limit as n approaches infinity of 3^n7^{-n} ?

The limit as n approaches infinity of 3^n7^{-n} is 0

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limit as n approaches infinity of 3^n7^{-n}

n \to \infty lim (3^{n} 7^{- n})

0

Solution steps

n \to \infty lim (3^{n} \cdot 7^{- n})

Simplify

7^{- n} : \frac{1}{7 ^{n}}

= n \to \infty lim (3^{n} \cdot \frac{1}{7 ^{n}})

Simplify

3^{n} \cdot \frac{1}{7 ^{n}} : (\frac{3}{7})^{n}

= n \to \infty lim ((\frac{3}{7})^{n})

Apply the common limit:

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

= 0

x \to 9 - lim (x^{2} + 5 x + 7)

y^{^{''}} + 12 y^{^{'}} + 36 = 0, y (1) = 0, y^{^{'}} (1) = 1

y^{^{'}} + y = (x + 1)^{2}

\int \frac{10}{x ^{2} + 1} d x

\int \frac{x ^{2}}{( x + 6 ) ^{3}} d x

What is the limit as n approaches infinity of 3^n7^{-n} ?
The limit as n approaches infinity of 3^n7^{-n} is 0