What is the limit as x approaches infinity of (e^x)/(pi^x) ?

The limit as x approaches infinity of (e^x)/(pi^x) is 0

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limit as x approaches infinity of (e^x)/(pi^x)

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

0

Solution steps

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

Apply exponent rule:

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

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

Apply the common limit:

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

= 0

x \to 0 lim (\frac{1}{x - 5})

x \to - 1 lim (\frac{3 x + 2}{1 - x})

x \to \infty lim (\frac{x ^{2} - 1}{8 x ^{2} - 5})

x \to 0 lim (\frac{tan ( 4 x )}{sin ( 6 x )})

x \to - 2 lim (6)

What is the limit as x approaches infinity of (e^x)/(pi^x) ?
The limit as x approaches infinity of (e^x)/(pi^x) is 0