The purpose of this project is to solve the game of Light’s Out! by using basic knowledge of Linear algebra including matrix addition‚ vector spaces‚ linear combinations‚ and row reducing to reduced echelon form. | Lights Out! is an electronic game that was released by Tiger Toys in 1995. It is also now a flash game online. The game consists of a 5x5 grid of lights. When the game stats a set of lights are switched to on randomly or in a pattern. Pressing one light will toggle it and the lights
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Philippine Normal University Taft Avenue‚ Manila S.Y. 2013-2014 GRAPH OF COSINE FUNCTION (Semi - Detailed Lesson Plan) Submitted by: Rañola‚ Rachel L. III – 18 BSE Mathematics Submitted to: Prof. Imperio FIELD STUDY PROFESSOR September 13‚ 2013 I. TOPIC: GRAPHING COSINE FUNCTION Subtopic: Properties of Cosine Function Shifting of the graph References: 1. Advance Algebra‚ Trigonometry and Statistics
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MATH 152 MIDTERM I 02.11.2012 P1 P2 P3 Name&Surname: Student ID: TOTAL Instructions. Show all your work. Cell phones are strictly forbidden. Exam Duration : 70 min. 1. Show that 1 p n (ln n) n=2 converges if and only if p > 1: Solution: Apply integral test: Z Z ln R 1 X R 2 1 p dx x (ln x) p=1 p 6= 1 let ln (x) = u then ln 2 so that when p = 1 and p < 1 integral diverges by letting R ! 1‚ so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln
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C3 Coursework Numerical Methods In this coursework I am going to investigate numerical methods of solving equations. The methods I will use are: 1. Change of sign method‚ for which I am going to use decimal search 2. Fixed point iteration using x = g(x) method 3. Fixed point iteration using Newton-Raphson method I will then compare the methods in terms of speed of convergence and ease of use with hardware/software Contents |Change of sign
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UNSW Econ 1202/2291 Quantitative Analysis For Business and Economics Examples Covered in Lectures 2011 WARNING! 1. These examples were given as part of a Lecture. To look at them outside of their original context would be reckless. Be sure to understand these examples in the context of the lecture material. 2. Since they are Lecture examples‚ they are subject to the constraints of lectures: they do not aim to illustrate all the techniques that you are expected to master in the course. 3. Lecture
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1) 5/5 Classify as a polynomial‚ a power function‚ or a rational function. y = x/(x+1)^2 (5pts) Polynomial Power Function Rational Function Collapse 2) 5/5 Sketch a graph of the function. Find the x and y intercepts. f(x) = -x^3 + 1 (5pts) x-intercepts (-1‚ 0) (1‚ 0) y-intercept (0‚ 1) x-intercept (1‚ 0) y-intercept (0‚ 1) x-intercepts (-1‚ 0) (1‚ 0) y-intercept (0‚ -1) x-intercept (-1‚ 0) y-intercept (0‚ -1) Collapse 3) 5/5
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Continuity and Differentiability Extra questions: 1) If f(x) = is continuous at x = 0‚ find the value of a and b 2) A function f is defined as f(x) = for x 1 = - for x = 1. Show that f(x) is differentiable at x = 1 and find its value 3) Let f(x) = if x 2 = k‚ if x = 2. If f(x) is continuous for all x‚ then find the value of k. 4) Let f(x) be a function of x defined as f(x) = ‚ x 1
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MATHS IN DAILY LIFE Mathematics is an integral part of our life. Right from the time we wake up in the morning till we go to sleep‚ invariably we are using mathematics in one or the other way. Teaching mathematics in classroom using pictures from daily life can help students in understanding a concept in a better manner. For instance‚ when a child is introduced the concept of 3 dimension‚ he/she is not able to visualize it. Learning of this concept can be made simpler and interesting by showing
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Chapter 1 THE PROBLEM AND ITS BACKGROUND Introduction Mathematics is a very important subject. The effect of Mathematics in our daily struggles in life is very evident. Everything involves Mathematics that is why Mathematics is very important on the part of the students to study. Over the years‚ schools have always been concerned with the development of effective learning experience for the learners. It is generally accepted that the quality of education students get largely dependent upon
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KISII UNIVERSITY COLLAGE FACULTY OF EDUCATION INTRODUCTION TO MATHS CONCEPTS COURSE DESCRIPTION The course will cover the units that enable the teachers to stimulate intellectual curiosity and independence‚ develop reading skills‚ motivation and study habits which are essentials for continuous independent learning and teaching mathematics. Apart from the basic concept of mathematics‚ a deeper concentration will be done on psychological bases for teaching learning mathematics‚ furthermore relating
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