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.