Canceling infinity - posted sort of late

I don't know why I never posted this back when I wrote it in October, but I'm posting it now.

Surprisingly, my post about taking limits hit almost as many nerves as the ones about Dunkin' Donuts. Anonymous, for example, got all up in my grill and may have called me stupid, but I can't be sure because his/her comment is unclear. And, amusingly, my friend told me that when she read the post to her husband, he, too, got all upset about my "plugging in" and "canceling" infinity. Because you can't! You can't cancel infinity! What about the limit of sin(x)/x as x approaches 0?, hmm? WHAT THEN? ("Yeah!" The Husband is probably shouting as he reads this.)

So, yeah, Friend's Husband has a point. Sometimes you have to use L'Hopital's rule first. But eventually, just plug in infinity and roll with it.