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?
- The difference is that when you find the limit of a function at x=c, you are aiming to find the y value as you approach c. However, the limit does not necessarily mean finding the limit of a point. A limit can still be found at a discontinuity such as a "hole". On the other hand, when PLUGGING in the number at x=c, there will be an exact point or output and there will be continuity at that point. They are the same when the function is continuous.


2.What are the SIMILARITIES between finding the derivative and finding the slope of a line? What are the DIFFERENCES between the two?
- The similarities are that a derivative and a slope are the change of y/change of x.

-The difference is that a derivative finds the slope of a curve's tangent line at one point and a slope finds the m of a simple line at two points. (when finding the derivative of a tangent line, you first have to find the slope of the secant line and then the take the limit of the secant line's slope to find the slope of the tangent)