Test Corrections (10/18/10)

1
Test Corrections (10/18/10)

• You can correct your mistakes, receiving 1/3 of
  the lost points back.
• Correct on a separate sheet, NOT on the original.
  Hand both in.
• Corrections are to be done on your own honor
  code or with help from me only. No
  collaboration allowed!
• Due at class Monday (Oct 25).

2
Some Tips As We Move Ahead

• If you practice, you WILL improve your
  pre-calculus skills (algebra, trig, etc.), BUT
  YOU MUST PRACTICE!
• Sit down and do the daily assigned exercises for
  EVERY class. Ask questions (in and out of class)
  if you dont get them.
• Once again, try doing the hand-in homeworks ON
  YOUR OWN, AND DO NOT LEAVE THEM UNTIL THE LAST
  MINUTE!

3
Calculus Versus Pre-Calculus

• As we move into calculus, you have the
  opportunity to start fresh with new ideas, so
  take advantage by working hard on these.
• However, we MUST be able to do pre-calculus well
  in order to do calculus, so we must continue
  always to work on those skills and concepts.

4
More on Limits

• Limits concern whats going on near , but not at
  , the point that the independent variable is
  approaching.
• Example Suppose f (x) 3x 1 if x ? 2
  10 if x 2Then what is limx ? 2 f (x) ?
  10? 7? Does not exist?

5
Clicker Question 1

• What is limx ? 3 x 2 if x ? 3
  5 if x 3 ?
• A. 5
• B. 3
• C. 9
• D. 6
• E. Does not exist

6
One-sided Limits

• If we are care about x coming into a point from
  the right , we have a one-sided limit.
• For example, we may say limx ? 2 f (x), meaning
  that x is coming in from the plus side.
• Likewise, limx ? 2? f (x) means were coming in
  from the left or negative side.
• The limits weve had before are called,
  naturally, two-sided limits. Note that these
  may not exist if the one-sided limits dont match
  up!

7
Clicker Question 2

• What is the limx ? 0- f (x ) for the function
  pictured on the board?
• A. 2
• B. 0
• C. -2
• D. Does not exist

8
Clicker Question 3

• What is the limx ? 0 f (x ) for the function
  pictured on the board?
• A. 2
• B. 0
• C. -2
• D. Does not exist

9
Assignment for Wednesday

• Begin correcting your test. Work carefully. Learn
  from your mistakes!
• Make sure have absorbed all the ideas of Section
  2.2 and have done all the exercises assigned last
  time.