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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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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St Hunter’s High School 12 Hunters Drive‚ Kingston 10 974-1421 July 12‚ 2013 Mr. Thomas Curelli Director‚ Maths Technological Resource Center 2b Lilliford Avenue‚ Kingston 10. Dear Mr. Curelli: We are requesting your presence at the St. Hunter’s High School first math enrichment seminars. The event is dubbed: Bringing Mathematics to life in the classroom- Hands-on approach to teaching Mathematics. We are requesting your presence on the second day November 19‚ 2013 of this three day
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Anopheles Quadrimaculators Vectors: Organochloride DDT and Global Malaria Paper on Organochloride’s Effect on Global Malaria Dr. Stephanie P. McCallum Ed.D. Environmental Health Public Health 8165 -1
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PART 11: FUNCTIONAL ANALYSIS In formulating the model‚ the system used t o i n t e r r e l a t e data i s called Functional Analysis or Value Engineering‚ plan through which data a r e collected. I t consists of a step-by-step job A verb noun language‚ o r function language‚ i s developed t o precisely describe what the product does; cost‚ energy and user a t t i t u d e s are allocated t o these functions; a function comparison i s made; c r e a t i v i t y by function can be carried
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