Limits and Derivatives..

1. When finding the limit of a function at x = c, you are finding the outputs that gets closer and closer to c from the negative and positive side. This will give you an approximate answer.

When plugging in the number x = c (or f(c)), you are finding the exact output at that number. This is basically your y and now you have a specific point.

One case in which the two are the same is when there is a removable discontuinity. This can be proven by the formula, lim f(x) x -> c- = lim f(x) x -> c+ = f(c). As the points from the negative and positive get closer to x, it will equal to c.

2. Derivatives and a slope of a line are similar because a derivative is the slope of a line. To be able to find the derivative at a certain point, you first need to find the slope of line that points is in. In both, you are finding the change of y over the change of x.

But they are also different because the deravative can be treated as the slope of a tangent line at a certain point, curved or not, but the slope of a line can be any common line.

My Limit..!

1. Finding a right and left end behavior model for a given function.
I understand it a few times but I need more clarification.

Ex.) f(x)=x+lnx

I know that you need to know how each graph looks like but from there, I get stuck.

2. Questions that involve finding the discontinuity.
I get stuck when it comes to questions like this because I don't know what to do.
Empty dot and fill-in dots throw me off.
Sometimes the questions that use piecewise confuse me.
For example, on Pg. 95, question 29.
I don't know why when x=0 and x=1 it is discontinuous.

3. Finding the horizontal asymptotes.
I sometimes know what they are because I already know how the graph looks like (e.g. f(x)= 1/x).
But I don't know what to do when given a more complex fucntion.
I rememeber one question I had trouble with was the last Free Response on our last test.
I forgot the function but I remember I couldn't find the horinzontal asymptotes.