Functions to Know in Calculus

Calculus is part of mathematics that deals with change. In algebra, you learned how to graph polynomials while in calculus you will learn how the graphed curve of polynomials change direction at each point.


Limits are the first topic when we study the calculus. Limit is the sequence 1/2, 1/3, 1/4 etc. It is obvious that limit of this sequence is zero. It is not part of the sequence but can get as close to zero as you want to go far enough in the sequence.


The derivative of a function describes how the function changes at each point. If D is derivative of a polynomial P, plugging a point into D will give the slope of the line which is tangent to the curve at that point. If we have polynomial Y = X^2, this is parabola that goes through points (1,1) and (2,4). The derivative of X^2 is 2X, and the slope of the tangent line at the point (1,1) is 2X = 2(1) =2, and the tangent line that goes through (1,1) is Y = 2X-1.


Integrals and derivatives are inverses of each other. That says fundamental law of calculus. If function F is graphed, the area between the curve and the X axis is given by the integral of F. If you use the calculus integral function, you will find the area of anything you have and equation to describe.


Exponentials have a big role in calculus function, as much as logarithms which are the inverse of exponentials. They are usually part of the solutions to deferential equations. Those equation have derivatives in them. If we have, for example Euler’s number, e^X, e^X = the derivative of e^X = the integral of e^X.

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