Limits with Euler's Number

Make a temporary $y$ variable, and perform ${\lim }_{n\to \infty }\ln y$ or ${\lim }_{n\to \infty }{e}^y$, then undo the operation.

Example

1. ${\lim }_{x\to \infty }(x-\ln x)$
2. $y=x-\ln x$
3. ${\lim }_{x\to \infty }{e}^y$
4. $={\lim }_{x\to \infty }{e}^{x-\ln x}$
5. $={\lim }_{x\to \infty }\frac{e^x}{e^{\ln x}}$
6. $={\lim }_{x\to \infty }\frac{e^x}{x}$
7. $=H={\lim }_{x\to \infty }\frac{e^x}{1}$
8. $=\infty$
9. $y=\ln (\infty )$
10. $y=\infty$