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?

Difference- when you are finding the limit you are finding the y value that wouldbe at x=c, if there was no discontinuity in the function. But, when you actually plug in the number x=c, you will get the output.
For example if there is a removable discontinuity at x=2 in a function, the limit might turn out to be 1, while if you plug in 2 into the function you might get an output of 3.
Same- the two are the same when there is no discontinuity at x=c and the limit is the same as the output of the function.



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

Similarities- the derivative of a line and the slope of the line are basically the same thing: the change in y over the change in x.
Differences- I'm fairly sure that the differences in the two are in where the derivative and the slope are used.
For example, finding the slope of a parabola, would give you the value of the slope of the parabola's secant line, while finding ther derivative of that same parabola would give you the slope of the parabola's tangent line.