Post 19

Ok, so looking back at my notes from the beginning of the year, I realized how simple limits and derivitaves and limits were/are. When we first covered them, they seemed to be so hard, but looking back on it now I really understand them.

Ok, first of all, limits. Limits are used to find where an x value is going on a graph. There are two different kinds of limits, limits that appraoch infinity or negative infinity or limits that approach a number. If you are solving a limit approaching infinity, you do these things:

1. If the degree of the top is larger than the degree of the bottom, the limit approaches infinity

2. If the degree of the bottom is larger than the degree of the tip, the limit approaches zero

3. If the degree of the bottom is equal to the degree of the top, then you make a fraction out of the coefficients in front of the largest degrees

Limits approaching numbers can be solved/found in a few different ways. First, you can plug the number x is going to into the x values of the limit and see what it comes out to be. Sometimes you can do this and come out with an actual number, but other times, the bottom comes out to zero. Many people think this means the limit is undefined, but this is not always correct. If the limit comes out to be zero, you have to use other methods to solve it. Another easy way to solve a limit is to try to break up the limit and cancle what you can, then plug in your x value. If this does not work, then you would have to plug in the limit into your calculator. If you are working with the definition of a derivative, all you have to do is take the derivative of the last term, and that is your limit

For derivatives, I will give an example

x^4 + 3x^3 + 6x

Ok for derivatives, you multiply the coefficient in front of your variable by it's exponent, then subtract 1 from your exponent.

4x^3 + 9x^2 + 6

There is also the first derivative test:

1. take first derivative

2. set equal to zero

3. solve for critical values

4. set up intervals

5. test intervals

The first derivative test can be used to find critical values on a graph, makimums, and minimums.

There is also a second derivative test. It has the same steps as the first derivative test except you take two derivatives instead of one. You can use the second derivative test to find points of inflection on a graph and where the graph concaves up or down.

I'm still a little shaky on linerization and I still absolutly do not understand angle of elevation