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Derivatives of Trig Functions Trigonometry can be intimidating for some students, but we’ll only be looking at the derivatives of sine, cosine, tangent, and other trigonometric functions. Just finding the slope of a tangent line, increasing the number of things we can take the derivative of, incorporating them with our products and our quotients. [Graph]…

Mean Value Theorem The mean value theorem states that if f(x)=g(x) for all x in some interval containing a and b, then there exists at least one number c in this interval such that f(c) =g(c). Now let’s talk about some definitions and equations. An average rate of change can be expressed algebraically as the…

Quadratic approximation Quadratic approximation is used to determine the change in a function f of (X,y) when x and y are changed a little bit. It can be expressed as the sum of two terms: the first-order term and the linear term. The first-order term is f sub x times the X change in X,…

Limits Involving Infinity. Example Problem 2 In this case, we’re dealing with a negative infinity. The graph could have no asvmptotes, or a horizontal asymptote of zero or some finite value of y. We will now look at the largest degree of the numerator and denominator. The largest degree of the numerator is four. The…

How to Read Mathematical Formulas In order to understand the mechanics of mathematical formulas, it’s important tonknow the conventions regarding the order in which logical operators apply. As a quick summary, the precedence order for applying logical connectives is as follows: (forall L)..(..) (exists L) (…) Quantifiers are the words that bind tightly, that hold…

Cartesian Plane – Plotting Points The Cartesian plane is a two-dimensional coordinate system that has two axes, X and Y. The X axis represents the horizontal axis, and the Y axis represents the vertical axis. The point here is really simple. These are called coordinate axes. Each of them has an origin point (this point…

Quantifiers Quantifiers are used in mathematics to express and prove facts. The two quantifiers are: There exists, and for all. These are all we need to look at because of the special nature of mathematical truths. When mathematics is viewed as a subject in its own right as opposed to being a set of tools…

Simplification Rules for Algebra using Exponents Five simplification rules for exponents will help you keep notation straight and do algebra using exponents. Practice these five rules, and you’ll be able to solve just about any algebra problems that contains integer exponents. We’ll discuss five rules for simplifying exponential expressions. Then we’ll look at a number…

Parallel and Perpendicular Lines Parallel lines are lines that run in the same direction and never cross.Perpendicular lines are lines that intersect at right angles. Example 1: Graph the following lines on the grid below. a) y=2x-3Slope = 2y-intercept = -3Plot they intercept =-3Use the slope to get a point m=21or-2-1y=2x+1Slope = 2y-intercept = 1Plot…

IB Chemistry: Chemical Equations Deduce chemical equations when all reactants and products are given. The process up there is basically a reaction. A reactant forms a product. We’re going to learn how to “deduce” a chemical equation when the reactants and products are BOTH given. A Chemical Reaction is basically a reaction between reactants to…