Question

Use l'Hospital's Rule to find the value of the limit.

Answer 1

\[\lim_{x \rightarrow \infty}(1+(6/x))^x\]

Answer 2

$$e^6$$

Answer 3

I really need help getting an understanding of this Rule please....how often are you on this website?

Answer 4

depends

Answer 5

oh ok!

Answer 6

$$\lim_{x \rightarrow \infty}\left(1+\frac{6}{x}\right)^x$$

$$\lim_{x \rightarrow \infty}e^{x\ln\left(1+\frac{6}{x}\right)}$$

$$e^{\lim_{x \to \infty}x\ln\left(1+\frac{6}{x}\right)}$$

Answer 7

so compute

$$\lim_{x \to \infty}x\ln\left(1+\frac{6}{x}\right)$$