Math 221 L’Hôpital’s Rule Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

L’Hôpital’s Rule is a tactic for finding certain limits by using derivatives. See section 4.8 in our textbook for a description and examples of the rule. This discussion gives you some experience using L’Hôpital’s Rule.

See if you can use L’Hôpital’s Rule to find...

1. $$\underset{x\to 0}{lim}\frac{e^x-1}{x}$$
2. $$\underset{x\to \mathrm{\infty }}{lim}\frac{x}{e^x}$$
3. $$\underset{x\to \mathrm{\infty }}{lim}\frac{x}{\ln x}$$
4. $$\underset{x\to \pi }{lim}\frac{x^2-\pi x}{\sin x}$$

If you evaluate

without using L’Hôpital’s Rule, what do you get? If you apply L’Hôpital’s Rule to that limit, what do you get? I expect the answers to differ — can you explain why, and which one is right?