# What is #lim_(xrarrtheta)(xcostheta-thetacosx)/(x-theta)#?

##### 3 Answers

Use L'Hôpital's rule. The limit is

#### Explanation:

Whenever the numerator and denominator of a limit both approach 0 (or both approach *rate* at which they approach 0 (or

**Example:** It's easy to see that *rate* at which the numerator is approaching 0 is *twice* that of the denominator, meaning our limit is 2 (which matches our answer from before).

So:

By l'Hospital's rule the limit is

#### Explanation:

Apply l'Hospital's rule and find

The reasoning may be more clear if we replace

#### Explanation:

then