Contents Pages OBJECTIVES 3 ACKNOWLEDGEMENTS 4 INTRODUCTION 5 PART 1 6 PART 2 7-12 PART 3 13-17 FURTHER EXPLORATION 18-19 REFLECTION 20-21 OBJECTIVES We students taking Additional Mathematics are required to carry out a project while we are in Form Five. This project can be done in groups or individually‚ but each of us is expected to submit an individually report. Upon completion of the Additional Mathematics Project Work‚ we are to gain valueable experiences and able to:
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Newton’s Method: A Computer Project Newton’s Method is used to find the root of an equation provided that the function f[x] is equal to zero. Newton Method is an equation created before the days of calculators and was used to find approximate roots to numbers. The roots of the function are where the function crosses the x axis. The basic principle behind Newton’s Method is that the root can be found by subtracting the function divided by its derivative from the initial guess of the
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FKB20203 Engineering Technology Mathematics 2 Lecture 2: Limits and Continuity Lecturer: Norhayati binti Bakri ( (norhayatibakri@mfi.unikl.edu.my) WEEK 2 Objective: To evaluate limits of a function graphically and algebraically To determine the continuity of a function at a point Limits (a) (b) A 1. in everyday life in mathematics Limits – Graphical Approach Examples f(x) = x + 2 x+2 ‚ x ≠ 2 h(x) = ‚ x=2 3 7 6 5 4 3 2 1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5 g(x) = x2 − 4 x
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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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