"Sum It Up"

The three major concepts in AP Calculus that I have learned of so far are Derivatives, Definite Integrals, and Limits. A derivative is the slope at a precise point on a graph which is sometimes referred to as the Instantaneous Rate of Change. A method for finding the derivative is the Change in Y⁄ Change in X(slope). Besides derivatives another mathematical term I have learned is definite integrals. An integral is the area between a function and the x-axis. Through a process of counting trapezoids on the graph the definite integral can be determined. The equation

(b₁+ b₂ ⁄2)h is applied when using the trapezoid method. The last concept is Limits which is defined as when you have a "x" value or something very close to it the function is very close to a certain "y" value. For example the chart below shows that if these points were on a graph the limit at one would be four (lim_x→1 f(x) = 4). A limit can be calculated by using the Average Rate of Change and can be proven by using the "Finger Test".

Example of a limit:

lim_x→1 f(x) = 4