QuestionMath 190
Analytic Geometry and Calculus 1
6. Extra credit: Evaluate the limit $$\lim _{x \rightarrow \infty}\left(1+\frac{5}{x}\right)^{3 x}$$

Studdy Solution
Now, since $\left(\left(1+\frac{5}{x}\right)^{x}\right)^3$ is equivalent to $(e^5)^3$, evaluate the limit:
$$\lim_{x \rightarrow \infty} \left(1+\frac{5}{x}\right)^{3x} = (e^5)^3 = e^{15}$$
The value of the limit is:
$$\boxed{e^{15}}$$