Hand out

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As we head into something new, this handout of Algebraic Limit Rules is handy (which was given to us on Friday)

Limits and Functions

Suppose that limits

exist and let "c" be a constant

CMR (Constant multiple rule)

The limit of a constant times a function is the constant times the limit of the function

lim c f(x) = c lim f(x)

SR (Sum of Function Rule)

The limit of a sum is the sum of the limit

lim (f(x)+g(x)) = lim f(x) + lim g(x)

DR (Difference of Function Rule)

The limit of a difference is the difference of the limits

lim (f(x) - g(x)) - lim f(x) - lim g(x)

PR & QR (Product of Function and Quotient of Functions Rule)

PR: lim (f(x)g(x)) = (lim f(x))(lim g(x)) QR: lim (f(x)/g(x)) = lim f(x)/lim g(x)

Example 1:

Example 2:

Example 3:

Note:

The limits are the same but the function itself is different, for

f(x) = (x

^{2}/x-1 - 1/x-1) there is a discontinuity at x = 1

For more examples similar to these one look at example 2 and 4 in the Algebraic Limit Rules booklet.

Example 2

Example 4

Homework: Exercise 2.7

1-9 (odd)

14-27 (odd)

and 24

And now it is time for the ROFL corner!

Since the last riddle was a tad difficult, I'll give you guys an easier one, which means that you won't need a hint for this one. ;D

How many times can you take 5 out of 25?

And if that one is too easy try this one! (Sorry!! I don't have a hint for this one!)

What belongs to you, but is mostly used by others?

Have fun!

Finally the next scribe will be...... Hi I'm Justice!

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