Mean Girls and Math

So you all know about Mean Girls. Cady Heron is a new girl at school and joins the Plastics and essentially wreaks havoc in her new high school. But at heart, she is a math nerd, like me. So before she heads to the dance, she is at a math competition. Before I complain that none of the math competitions were anything like the one in Mean Girls, I would like to complain that the final question was not that difficult.

So they have to find out the limit as x approaches 0 of the natural logarithm of (1-x) minus sine of x divided by sine of x quantity squared or 1 minus cosine of x quantity squared.This is not an easy problem, but for a math team, this should be child's play. It does require l'Hopital's Rule because the first limit is indeterminate (0 divided by 0, infinity divided by infinity). What I am shocked at is that the other person guessed -1. I haven't looked that much into it, but I did use WolframAlpha to look at the plot.

It does not approach -1 whatsoever. Maybe 1 or -5, but -1? Really Tina Fey? I guess I'm just nitpicking at math in movies, because I do love math and movies. But I was shocked at complete lack of thought put into that scene. I also would like to know how Cady Heron somehow managed to get the right answer. My first problem is that there was only one instance of them learning limits. I've taken calculus and for one semester, the bulk of the learning was covering limits. Next problem is that how did she know that the limit was an infinite limit? I guess that she could intuit it, but considering that she answered after Ms. Kraft (granted she was a tad distracted through her monologue) should say something about what she knew. So note to future movie writers, get your math right or else.