Teaching High School Mathematics
A close variation of appeared on the AP calculus email list recently and so I thought I’d try to work up the solution here. I’ve used LaTex before and have really enjoyed using it, but sometimes it’s hard to know what to type to get the exact math typesetting your looking for. While I was typing this post I posted with one equation to see what it looked like. I came back later and I had a comment from CrazedMummy with a link to an awesome resource for LaTex code. you just draw the math equation and wahla, it gives you the code. WebEquation is great! Thank you CrazedMummy, I will use this a ton. It has now already been well worth it to start blogging. Thanks Sam.
On to the problem…
In order to solve this problem we need to start with the idea that the sine of anything is between or equal to one and negative one.
Then we need to multiply all three parts by .
Because is always positive or zero, multiplying by one and negative one keep it the same except the negative, and since sine is always between negative one and one, multiplying by will keep it between and .
Graphically this looks like:
You then take the limit as x goes to zero of all parts.
because it has to be between 0 and 0.