What is the limit as x approaches infinity of ((13x)/(13x+3))^{5x} ?

The limit as x approaches infinity of ((13x)/(13x+3))^{5x} is 1/(e^{15/13)}

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limit as x approaches infinity of ((13x)/(13x+3))^{5x}

x \to \infty lim ((\frac{13 x}{13 x + 3})^{5 x})

\frac{1}{e ^{\frac{15}{13}}}

Decimal Notation

0.31542 \dots

Solution steps

x \to \infty lim ((\frac{13 x}{13 x + 3})^{5 x})

Apply exponent rules

= x \to \infty lim (e^{5 x l n (\frac{13 x}{13 x + 3})})

Apply the Limit Chain Rule:

\frac{1}{e ^{\frac{15}{13}}}

= \frac{1}{e ^{\frac{15}{13}}}

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What is the limit as x approaches infinity of ((13x)/(13x+3))^{5x} ?
The limit as x approaches infinity of ((13x)/(13x+3))^{5x} is 1/(e^{15/13)}