Limits

This past week of school we were introduced to Calculus. Our first lesson was in Chapter 19, on Limits. The lesson was pretty simple because we did lessons on limits in advanced math.

Notes to take:

A limit is a singular y-value.

-To find a limit, plug into the equation. If you have 0 on the bottom and 0/0, you have to try doing something else.

Other options:

1-Graph (infinite/-infinite is still considered a (y) value.

2-Use the table:

x-.1, x-.01, x-.001, x, x + .001, x + .01, x + .1

à              ß                              

   

3-Trying to factor and cancel something (algebra).

Examples:

11)   Lim x->4

x-4 / x^2-3x-4

x         3.9     3.99    3.999  4.001   4.01    4.1

f(x)   .209   .2009  .2009   1.9996 1.996  1.96

From doing the table, you can see that as the table values approach x, it gets closer to .2. Therefore, .2 is the answer.