Test Corrections (10/17/11)

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 24).

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 don’t get them.

Once again, try doing the hand-in homeworks ON YOUR OWN.

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.

More on Limits Limits concern what’s 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 = 2

Then what is limx 2 f (x) ? 10? 7? Does not exist?

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

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 we’re coming in from the left or negative side.

The limits we’ve had before are called, naturally, “two-sided” limits. Note that these may not exist if the one-sided limits don’t match up!

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

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

Assignment for Wednesday

Begin correcting your test. Work carefully. Learn from your mistakes!

In Section 2.2, please do Exercises 2, 5, 7, 15