AP Calculus

1/4/10 MW

January 6th, 2010

Posted in Passed Entries, Scribe:Matt || 2 Comments »

Class Notes 12/17 EG

January 6th, 2010

We worked on related rates packet. The problem below is from the first page of the packet.

NO HOMEWORK, VACATION!!!

Posted in Passed Entries || No Comments »

Related Rates 12/17 LizF

December 17th, 2009

During class we did a group quiz re-take. Then Mrs. Everard quickly introduced Related Rates.
Hw is finish the MC
Example number 1 from page 517
Find how fast z is changing when x=10

600=rate of change for x

Posted in Scribe:Liz || No Comments »

kh 12/11

December 14th, 2009

Derivative=Continuity≠ Differenciation

Hw pg 158 problem 31

pg 161

Posted in Class Discussions, Class Notes and Assignments, Passed Entries, Scribe:Kayla || No Comments »

Class Notes: 12/7

December 10th, 2009

Derivative of Inverse Functions:

Restrictions on the domain of the original function

Restrictions on the range of the inverse function

Graph:

Inverse of Inverse Tangent:

Inverse of Cosecant

Graph of Inverse Cosecant:

Inverse of Cotangent:

Graph of Inverse Cotangent:

Sample Problem:

Answers to 14-24 on Pg.151

Hw: Do 13-33 Odd on Pg.157

Posted in Class Notes and Assignments, Scribe:Samantha || No Comments »

December 7th, 2009

Inverse Trigonometric Functions

*see page 148 for graphs

$\begin{eqnarray*} y & = & \tan^{-1}(x) \\ \tan(y) & = & x \\ \\ \sec^2(y) \frac{dy}{dx} & = & 1 \\ \\ (1 + \tan^2(y)) \frac{dy}{dx} & = & 1 \\ \\ (1 + x^2)\frac{dy}{dx} & = & 1 \\ \\ \frac{dy}{dx} & = & \frac{1}{1+x^2} \end{eqnarray*}$

$\begin{eqnarray*} \frac{d}{dx} \sin^{-1}(x) & = & \frac{1}{\sqrt{1-x^2}} \\ \frac{d}{dx} \cos^{-1}(x) & = & -\frac{1}{\sqrt{1-x^2}} \end{eqnarray*}$

$\frac{d}{dx} \tan^{-1}(x) = \frac 1{1+x^2}$

$\begin{align} \frac{d}{dx} \arcsin x & {}= \frac{1}{\sqrt{1-x^2}}\\ \frac{d}{dx} \arccos x & {}= \frac{-1}{\sqrt{1-x^2}}\\ \frac{d}{dx} \arctan x & {}= \frac{1}{1+x^2}\\ \frac{d}{dx} \arccot x & {}= \frac{-1}{1+x^2}\\ \frac{d}{dx} \arcsec x & {}= \frac{1}{x\,\sqrt{x^2-1}}\\ \frac{d}{dx} \arccsc x & {}= \frac{-1}{x\,\sqrt{x^2-1}} \end{align}$

HW: Derive inverse csc, sec, cot

Also: pg.152 13-21 odd

Posted in Class Notes and Assignments, Passed Entries, Scribe:Spencer || 2 Comments »

December 1 BJ

December 2nd, 2009

In class we went over the second Derivative Quiz and completed a worksheet on Implicit Differentiation.

Bonus problem on the quiz:

Calc Scribe Notes

Implicit Differentiation problem: #12 on pg. 171

Calc Scribe Notes 2

Homework:

- Read Section 4-5 on pgs. 145-148

- Review trig identities and the unit circle for a trigonometry quiz next class

Posted in Scribe:Brady || No Comments »

Natural Logs LizF

November 30th, 2009

In class we found the derivative of natural logs and exponential functions

Nat

Derived that the derivative for the natural log is one over the argument

So…

To find the derivative of an exponential function take the natural logs of both sides. Don’t forget that y is a function of x so the chain rule applies.