Algebra vs. Calculus

1. What is the DIFFERENCE between finding the limit of a function at x = c and actually plugging in the number x = c? When are the two cases the SAME.

~Finding limit at x=c, you are finding outputs that approach "c", your finding the "y" values of f(x)as x is approaching c. There can be a "hole" or what we call a "Removable Discontinuity", this "hole" can be covered with a piecewise function.
~When plugging in number x=c, there is an exact point. There is no "hole". You are finding the output(y) when x is equal to a constant.
-The two are the same when you take the limit of f(x) as x approaches "c".


2. What are the SIMILARITIES between finding the derivative and finding the slope of a line? What are the DIFFERENCES between the two?

~Change of Y divided by the change of X is the same when you are finding the slope of either one.

~Finding slope of a derivative involves many complicated equations of how to find tangent and secant lines, using LIMITS/: ,with using equations like that one below.../:


~Finding the slope of a line is easy, all you need to do is find the RISE/RUN...
In other words, find the change of Y over the change of X.