Algebra vs. Calculus

1. There is a difference between finding the limit as x aprroaches c than actually plugging in c into the function. In the function, there might not be a specific output when you input c, but when you are finding the limit as x aprroaches c you can find out a specific output. In other occasions, the function may have a output that when graphed, can not be seen where the limit is or a different output as the limit approaches c. There are cases when the output are the same because there is an exact output in the function for c.

2.Similarities in finding the derivative and the slope of a line is because you are finding the change of y over the change of x. When finiding a derivative, you are finding the slope of a tangent line to find out what is going to be your y value. The formulas are also similar, finding the slope of a line you need y1-y2/x1-x2, for finding the derivative its the same concept but a more complex way. They are different because when finding the derivative at a x, you are not finding the exact change of y over the change of x of the graph, but of the tangent line.