Question

lim_{x\to\infty}(1 + \frac{9}{x})^{\frac{10}{x}}

Explanation:

Step1: Use the formula $\lim_{x

ightarrow\infty}(1 + \frac{a}{x})^{bx}=e^{ab}$
Let $a = \frac{9}{1}$, $b=\frac{10}{9}$.

Step2: Calculate the limit

We have $\lim_{x
ightarrow\infty}(1+\frac{9}{x})^{\frac{10}{x}\cdot x}=\lim_{x
ightarrow\infty}(1 + \frac{9}{x})^{10}$.
Since $\lim_{x
ightarrow\infty}(1+\frac{9}{x}) = 1$, then $\lim_{x
ightarrow\infty}(1+\frac{9}{x})^{10}=1^{10}$.

Answer:

$1$