Page 112 - Calc for the Clueless

L'Hopital's rule applies. Taking derivatives of the top and bottom, we get (2x - 4)/(-10x), again going to .
Use our rule twice. The second time we get 2/-10 = -1/5. So our original limit was also -1/5.

Example 31—

We must do something algebraic so our wonderful rule can be used. In this case, we simply add the fractions
together.

L'Hopital's rule once gives us

Again, we get

So the original .

Sometimes when you take the limit, you get . In that case you must do something algebraic to get 0/0 or
.

Example 32—

Limit is .

We rewrite x sin (1/x) as

Now the limit is 0/0, and we can apply L'Hopital's rule.

Since

Well, that's all for now. The Calc II and Calc III will help you next. If you need algebra or trig review, get the
Precalc.