What is the limit as x approaches infinity of (e^{2x})/(5^{2x)} ?

The limit as x approaches infinity of (e^{2x})/(5^{2x)} is 0

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limit as x approaches infinity of (e^{2x})/(5^{2x)}

x \to \infty lim (\frac{e ^{2 x}}{5 ^{2 x}})

0

Solution steps

x \to \infty lim (\frac{e ^{2 x}}{5 ^{2 x}})

Simplify

\frac{e ^{2 x}}{5 ^{2 x}} : (\frac{e}{5})^{2 x}

= x \to \infty lim ((\frac{e}{5})^{2 x})

Apply exponent rules

= x \to \infty lim (e^{2 x l n (\frac{e}{5})})

Apply the Limit Chain Rule:

0

= 0

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What is the limit as x approaches infinity of (e^{2x})/(5^{2x)} ?
The limit as x approaches infinity of (e^{2x})/(5^{2x)} is 0