Calculus I

1
Calculus I

• Review of The Essentials

2
Homework

• Section 1.1 through 1.6
• Read pages 1-9, 11-21, 25-35)
• Do problems from Chapter Review (page 78) True -
  False Quiz 1 through 8, 1, 3, 4, 5, 8, 9, 16,
  17, 19, 21 (give a sketch of the scatter plot)
  22, 23, 25, 26,

3
Syllabus

• Materials
• Homework How to ask questions in class, boxed
  problems, and checking your work.
• Quizzes
• Opportunities
• BlackBoard

4
Math 52

• Located in LRC, 0.5 to 1 unit for doing your
  homework while being helped by a faculty member.
• Great study group location.

5
BlackBoard

• Logon and update your profile, email in
  particular, prior to Wednesday.
• Leave a message introducing yourself and why
  youre taking calculus in the Introduction Forum
• You can get 24/7 homework help from your friends
  on the web via BlackBoard, Extra credit towards
  homework for those that help!
• I will be building this resource as we go, so,
  check it often.

6
How to Read

• Reading a calculus text is a different
  experience.
• Lets read what Stewart has to say about it.
• Lets jump to page 72 and practice a bit
• YOU MUST READ THE TEXT.

7
More On Success

• Do a schedule! You need to plan the days and
  times that you study calculus and stick to it. It
  will take an additional 8 hours beyond class
  minimum to study this subject.
• If you sleep between 7 to 8 hours a night then
  you have between 112 and 119 hours each week to
  spend awake. You need to schedule calculus into
  those hours

8
More On Success

• Form a study group! In general the people who
  succeed in mathematics are the ones that study
  with other people. Learning is hard work but can
  be incredibly rewarding and enjoyable. This joy
  is only multiplied when it is done in a
  collaborative environment. Math 52 can promote
  this.
• Come to office hours and bring a friend. Going to
  a teachers office can be scary, take a friend
  with you.
• Take care of your self! Eat well, ride a
  bike,walk the beach, and smile. Your education
  should be something you love!

9
Lets Do Some Math!

• What is a function?
• What are the 4 ways to represent a function that
  are most commonly used?
• Give the four ways to relate the cost of taking
  classes at CR

10
A Useful Definition

• A function f is called increasing on an interval
  I if
• It is called decreasing on I if

11
Example

• Give the intervals of increasing and decreasing
  for the function

12
Regression Models

• Lets do an example from the text. Open to page
  37 and lets do problems 15, 16, and then 21

13
Your Calculator Can Tell Lies

• Enter y sin 96x and y sin 2x into your
  calculator using 0, 2p, -4, 4 with Xscl p/4
• Now change it to -p, 2p, -4, 4
• Notice anything strange?

14
Problem Solving

• A driver sets out on a trip at a leisurely pace
  of 30mph for the first half of the distance. She
  drives the second half of the journey at 60mph.
  What is her average speed on the trip?

15
f

• State the domain, the range
• Is f odd, even or neither?
• Is f one-to-one?

16

• An airplane flies from Arcata to San Francisco in
  an hour (no fog). The total ground distance was
  about 280 miles. If t represents the time in
  minutes since the plane left the ground, let x(t)
  be the horizontal distance traveled and y(t) be
  the altitude of the plane.
• Sketch a possible graph of x(t).
• Sketch a possible graph of y(t).
• Sketch a possible graph of the ground speed.
• Sketch a possible graph of the vertical velocity.