Fwd: Test

---------- Forwarded message ----------
From: Adam Boocher <aboocher@gmail.com>
Date: Wed, Oct 2, 2013 at 2:03 PM
Subject: Re: Test
To: CAROLINE RACHEL SISCHO <carolinesischo@berkeley.edu>

First:  This course has not taught trig functions, yet - so there's no need to worry about them. 

Secondly:  How do you compute the derivative of sin(x) in order to use l'hopital's rule?   I bet you know it's cosine, but the proof of the fact that the derivative of sine is equal to cosine actually relies on the fact that  lim (sin x/x) = 1.      (So usually l'hopital to do this is kind of cheating in my book.)

Finally:  The way you would compute this limit is using the squeeze theorem (which is too advanced for 16A) :  It's kind of hard to explain in email, but here's a few pages that talk about it: 

http://ime.math.arizona.edu/g-teams/Profiles/JS/Calc/SqueezeTheorem.pdf

There's also a 15 minute youtube video that came up on a google search.  I have no idea if it's good or not. 

But it's probably better for the midterm to just forget about this stuff :)  If you want to know sometime, come to office hours. 

-Adam 

On Wed, Oct 2, 2013 at 1:49 PM, CAROLINE RACHEL SISCHO <carolinesischo@berkeley.edu> wrote:

Then how would I solve the problem: limit as x approaches zero of sin (x)/x without using le hopitals rule? Thank you.

Caroline

On Wednesday, October 2, 2013, Adam Boocher wrote:

That is true.  Only chapter one techniques.  You shouldn't need l'hopital's though...

On Wed, Oct 2, 2013 at 1:45 PM, CAROLINE RACHEL SISCHO <carolinesischo@berkeley.edu> wrote:

Hi Adam,

Someone just told me we cannot use l'hopitals rule on the test. Just want to confirm this is true. Thank you.

Caroline