Question

The value of $\underset{x\to \infty }{\lim }{\left(\frac{x+5}{x-1}\right)}^x$ is

• A. $e$
• B. $e^3$
• C. $e^5$
• D. $e^6$

Answer 1

The correct option is D $e^6$

$\underset{x\to \infty }{\lim }{\left(\frac{x+5}{x-1}\right)}^x=\underset{x\to \infty }{\lim }{\left(1+\frac{6}{x-1}\right)}^x=e^{\underset{x\to \infty }{\lim }\frac{6x}{x-1}}=e^6$