Open House Reminder

Today was one of those days where we just pounded through various problems that we have encountered over the last few lessons.  Please read each of the reminders that I have posted below.

1)   Attention all grade 12 students, there is a Spring Open House at the University of Windsor, Friday March 9th from 11-4pm. (Yes this is the day before the start of March Break.)  You need to sign up on line.  Sign up at www.uwindsor.ca/openhouse or you can phone them at 519-973-7014.  You will get a free lunch at the student centre with your student id.  Don't forget to call into attendance to report your absence.

2)  We will be covering section 2.5 in class on Thursday.  Be sure to read about the Chain Rule prior to coming to class.

3)  Your unit test for Chapter 2 will be on Monday, March 5th.

4)  Any student interested in writing the University of Waterloo, Euclid Math Contest must speak to Mr. Adlam prior to the end of this week.  The deadline is quickly approaching and I need final numbers.

Quotient Rule

We took a look at how to differentiate rational functions in class today using the Quotient Rule.
NOTE:  The derivative of a quotient is NOT the quotient of their derivatives.  See the proof on page 94 of your student text for the proof of the rule.  If explanation is required ask in class tomorrow.

HOMEWORK:  Page 97 - 98, #'s 3, 4bcf, 5ab, 7, 8, 9b, 10 and 12

The plan is to move on to section 2.5 in class tomorrow.  If there are no questions regarding the Quotient rule we will start our study of the Chain Rule on Wednesday.  This would be the last section in the chapter, it is almost time for a test.

More with Product Rule

Today we looked at the proof of the Product Rule in more detail.  Again, refer to page 85 and 86 of your student text when looking at our lesson notes.

We also showed how to find the derivative of the power of a function.  That is if f(x) = [g(x)]^n than the derivatve will be f'(x) = n * [g(x)]^(n-1) * g'(x).  Again refer to the examples on page 88 and 89 for further clarification.

HOMEWORK:  Pg. 90 -91, #'s 1f (again), 2ad, 4, 5de, 9 and 10

NOTE:  We will be moving into section 2.4 tomorrow and looking at the Quotient Rule.  So read ahead to get a brief picture of where we are going.

Product Rule (Part I)

Today we began to look at how to use the product rule in order to differentiate the product of two seperate functions.  Be sure to re-read the proof of the product rule (using first principles) in your student text as we will look a little closer at that in class on Monday.

Bottom line if f(x) = g(x)h(x) in order to find the derivative you simply CANNOT multiple g-prime(x) by h-prime(x)...you NEED to use the product rule.

HOMEWORK:  Page 90 - 91, #'s 1bcdf, 5abf, 6 and 7

Have a great weekend everyone!  If you have any questions this weekend promise to answer them!!!

Derivatives of Polynomial Functions

 We started looking at Rules for Differentiating functions in class today.  Some of the lesson notes below simply are re-stating what is already written for you in your student text.  Re-read the proofs of the various rules for yourself.  If there are any steps that you don't understand please be sure to ask for clarification prior to the next test.  There will more than likely be one formal proof that you will be required to provide (probably one of either the constant multiple, constant function, sum or difference rule)

HOMEWORK:  Page 82, #'s 2, 3 and 4

You will probably be given time in class tomorrow to work on further problems from this section as I may not be in class due to PD.

Derivatives using First Principles

Today we took a second look at how we find the derivative of a function with respect to 'x'.  We used the First Principles def'n (ie. the difference quotient from chapter 1) to find the equation of the derivative in general.

We also investigated the idea behind where a function can be differentiable.  Be sure to re-read the examples in section 2.1 along with the lesson notes below to get a true picture of what has been covered.

HOMEWORK:  Again from Section 2.1:  Page 73 - 74, #'s 1, 3, 13 and 14

Also, it might help to read ahead into section 2.2 as we will begin looking at the differentiation rules starting tomorrow in class.

The Derivative Function (An Intro)

Thank you for continuing to stay ahead of me and reading the sections over before coming to class.  I almost feel as if I am the one slowing you folks down.  We did "jump" over a few concepts in section 2.1 that we may have to revisit prior to moving on but that can be worked out after the fact.

Here are the rough (and I really mean rough) lesson notes from class today.  Be sure to re-read the examples from your text (Pages 65 through 71) for a deeper understanding and come in with any questions on Tuesday.

HOMEWORK:  Pages 74 and 75,  #'s 5, 6, 7b, 10, 11 and 15

Have a great long weekend everyone!  I have marking to do :)

Parking Lot

If you have any further questions while you are studying, don't be afraid to post them below and I will get to them at some point tonight.  I will check periodically throughout the evening...I am watching 'Survivor' between 8 PM and 9 PM :)

Continuity

Be sure to re-read the KEY IDEAS on page 51.  Make sure you understand that in order for a function to be continuous at some point x = a, the following criteria must be met:

1)  f(a) is defined
2)  limit as x approaches a of f(x) exists
3)  limit as x approaches a of f(x) is equal to f(a)

HOMEWORK:  Pg 51 - 53
#'s 1 through 4 are basic communication problems that we technically have discussed in class
#'s 5, 6, 7, 8, 10, 13 and 14 are questions that you should attempt and ask for clarification as necessary.

More with Limit Properties (Day 2)

To evaluate limits you first have to identify which STRATEGY you want to use.

HOMEWORK: From the same section as last Thursday...Page 46 - 47, #'s 7, 8, 9 and 12

Properties of Limits (Day 1)

Here are the basic examples that we covered from the first part of section 1.5.  You should now understand Examples 1 through 4 on pages 40 and 41 of your student text.

HOMEWORK:  Page 45, #'s 1, 3 and 4.

I would also encourage you to read the remainder of the examples in this section (5 through 9) on pages 42 through 44.  This will only help you better understand where we are going in Monday's class.

Limit of a Function

Good class today...sorry I went to the bell...that happens when you try the "Investigations".  Make sure you actually look at the screen shots below.  We didn't get to the last page of the lesson.  Try that example on your own before going on to the homework (which can be found at the end of the post...in bold)

HOMEWORK:  Page 38  - 39, #'s 4bcef, 5, 6, 7, 8b, 10bef, 11b, 12a and 13

Rates of Change

Today's lesson shows a simple application of what was covered in class yesterday.  The instantaneous rate of change for a situation (that is the velocity) is simply the slope of the tangent to the curve at some point x = a.

HOMEWORK:  Page 29, #'s 1, 7, 9, 11, 15b and 17

As a reminder, try and stay a day ahead of me in terms of your reading.  We are moving into section 1.4 in class on Wednesday.

Slope of a Tangent

Today in class we looked at determining how to find the slope of a tangent by finding the limit as 'h' approaches zero for a difference equation.

Recall the steps)
i.  Find f(a)
ii.  Find f(a + h)
iii.  Evaluate lim [f(a+h) - f(a)] / h, where h ---> 0.



HOMEWORK:  Page 20 - 21, #'s 8c, 9c, 10b, 11f, 16, 20 and 21.  (Feel free to work on the others that are not assigned at your own leisure if the time permits)

Rationalizing Radical Expressions

This lesson was mainly a review of material covered in grade 11.  The concepts are needed though before we can begin our study of LIMITS, which we will get into sometime next week.

Don't forget, I will list any assigned homeowork at the end of each post below any lesson notes that have been inserted.

HOMEWORK:  Page 9, #'s 1cf, 2cd, 3bd, 5, 6d and 7b

Diagnostic Test Solutions

In case we went to fast taking these up in class today I have provided the solutions (as written by your peers) to the diagnostic test you were working on during the lesson.

HOMEWORK:  Read section 1.1 of your student text as we will be starting with that tomorrow.

Welcome!

You have successfully made your way to the 4U Calculus & Vectors blog.

Here you will find any lesson 'notes' that we create in class. I will also list homework on this page so even if you are away you should be able to keep up with the content in the course.

Feel free to post questions directly on the blog. I will do my best to respond to as many as possible in a timely fashion.

Now...get ready to enter the WORLD OF CALCULUS...