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Is the maximum inside or on the boundary? So let’s discuss why the distance between (2, 0) and (1, 1) is less than or equal to 1. If we say that x minus 2 squared plus y squared equals 1, then the distance from (2, 0) to (1, 1) is equal to 1. In other…

Probability Definitions and Notation Probability is a measure of the likelihood that an event will occur. It is numerically expressed as a number between 0 and I, where O indicates impossibility, and I indicates certainty. Probability can be understood as the relative frequency of occurrence of an event in a large number of trials. If…

Solving Simple Equations Goal: To learn how to solve simple or one‐step equaons. An equaon is a mathemacal statement that says two expressions are equal. Example: 4x+1=5, 2x+3=x-1An expression is a mathemacal term or a sum or difference of mathemacal terms that may use numbers, variables, or both. Examples: 2x+1,×3-2×2+5To solve an equaon means to…

Limits Involving Infinity. Example Problem 1 When doing limits to infinity, the only thing of significance is the degree of the numerator and the degree of the denominator. lim_(x-> infinity) (10x^3 +5x^2 -8)/(3x^6 +9x+2) [Graph] x->infinity y->0 (10x^3)/3x^6 1/infinity^3 -> 0 Horizontal Aymptote of y=0 In this problem, we’re looking at a numerator degree of…

Intermediate Value Theorem We're looking at the intermediate value theorem. We will apply the idea of continuity to the first of these theorems in calculus. What is Intermediate Value Theorem in Math? Intermediate value theorem (IVT) is a basic theorem of calculus that says that if f(x) is continuous on the closed interval [a, b]…

Continuity Let us now consider the calculus explanation of why a function is continuous. Continuity is a mathematical concept that refers to the ability of a function to be represented as a continuous line on graph. In other words, if you zoom in on any portion of the graph, it looks like a straight line….

IGCSE Edexcel Economics: Wages and Employment in a Free Economy Division of Labour This is a process where each worker specializes in doing a particular task. If people concentrate on those tasks they are most adequate and skilled at, a lot more can be produced. Advantages and disadvantages of division of labour: for the worker…

Identity matrix A matrix is a rectangular array of numbers or other data, usually arranged in rows and columns. A matrix can have any number of rows and columns. The most common type of matrix is the two-dimensional matrix, which has two dimensions (rows and columns). In mathematics and science, matrices are used to represent…

CFA Level 2 – Quantitative Analysis, Session 3 – Reading 13, Time-Series Analysis – LOS k (Practice Questions, Sample Questions) 1. Which of the following statements regarding unit roots in a time series is least accurate? A) A time series that is a random walk has a unit root.B) Even if a time series has a unit…

Optimization. Lecture A square with no lid is to be manufactured such that the surface area is 192 sq inches. What are the dimensions that would yield the largest volume? [Graph] v=x^2*h —————-> SA=192=x^2+4xh v=x^2 *(48/x – x/4) 192-x^2=4xh v=48x-(x^3 -4) (48/x-x/4)=h v=48-(3x^2/4)=0 ___________________ 48=3x^2/4 48/8-8/4=h 64=x^2 6-2=h=4 x=8 8x8x4 General Guidelines: 1) Make a…