What is the limit as x approaches infinity of (1+(11)/x)^{x/(12)} ?

The limit as x approaches infinity of (1+(11)/x)^{x/(12)} is e^{11/12}

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limit as x approaches infinity of (1+(11)/x)^{x/(12)}

x \to \infty lim ((1 + \frac{11}{x})^{\frac{x}{12}})

e^{\frac{11}{12}}

Decimal

2.50094 \dots

Solution steps

x \to \infty lim ((1 + \frac{11}{x})^{\frac{x}{12}})

Apply exponent rules

= x \to \infty lim (e^{\frac{x}{12} l n (1 + \frac{11}{x})})

Apply the Limit Chain Rule:

e^{\frac{11}{12}}

= e^{\frac{11}{12}}

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x \to \infty lim (x ∣ x ∣)

x \to 0 + lim (\frac{7}{x} - \frac{3}{x ^{2}})

x \to 0 lim (cos (x) - x)

x \to 0 + lim ((x + cos (x))^{\frac{4}{x}})

What is the limit as x approaches infinity of (1+(11)/x)^{x/(12)} ?
The limit as x approaches infinity of (1+(11)/x)^{x/(12)} is e^{11/12}