What is the limit as x approaches infinity of ((14x)/(14x+6))^{2x} ?

The limit as x approaches infinity of ((14x)/(14x+6))^{2x} is 1/(e^{6/7)}

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limit as x approaches infinity of ((14x)/(14x+6))^{2x}

x \to \infty lim ((\frac{14 x}{14 x + 6})^{2 x})

\frac{1}{e ^{\frac{6}{7}}}

Decimal Notation

0.42437 \dots

Solution steps

x \to \infty lim ((\frac{14 x}{14 x + 6})^{2 x})

Apply exponent rules

= x \to \infty lim (e^{2 x l n (\frac{14 x}{14 x + 6})})

Apply the Limit Chain Rule:

\frac{1}{e ^{\frac{6}{7}}}

= \frac{1}{e ^{\frac{6}{7}}}

x \to 0 - lim (\frac{6}{5 x ^{3}})

x \to 0 - lim (\frac{1}{x ^{15}})

x \to - 2 lim (π)

x \to 3 lim (3 x + 5)

x \to \infty lim (\frac{( x ^{12} )}{e ^{x}})

What is the limit as x approaches infinity of ((14x)/(14x+6))^{2x} ?
The limit as x approaches infinity of ((14x)/(14x+6))^{2x} is 1/(e^{6/7)}