University of Business Technology UBT – CEIT CALCULUS I – MATH 101 FALL – 2012 Instructor : Abdulraheem Zabadi STUDY GUIDE Table of Contents Limits Differential Calculus Integral Calculus SOME USEFUL FORMULAS Chapter One : Limits Properties of Limits If b and c are real numbers‚ n is a positive integer‚ and the functions ƒ and g have limits as x → c ‚ then the following properties are true. Scalar Multiple : limx→c (b f(x))=b limx→c fx
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motivation is the key to a better future generation. Besides that‚ I have very strong math skills‚ which help me make a strong candidate as a teacher. These math skills were visible when I took Calculus 1‚ and Calculus 2 in senior year of high school. After that‚ I took statistics and other advanced calculus classes in college. This progress continued through graduate school. Therefore‚ I believe that my educational math experience and previous experience as a math teacher will help definitely ensure
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two-dimensional coordinate system (and conversely‚ shapes to be described as equations) — was named after him. He is credited as the father of analytical geometry‚ the bridge between algebra and geometry‚ crucial to the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius. René Descartes’ Mathematical legacy One of Descartes’ most enduring legacies was his development of Cartesian or
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1.1.1 Show how to find A and B‚ given A+B and A −B. 1.1.2 The vector A whose magnitude is 1.732 units makes equal angles with the coordinate axes. Find Ax‚Ay ‚ and Az. 1.1.3 Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes. 1.1.4 The velocity of sailboat A relative to sailboat B‚ vrel‚ is defined by the equation vrel = vA − vB‚ where vA is the velocity of A and vB is the velocity of B. Determine the velocity
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Unit 1 Lesson 1: Optimization with Parameters In this lesson we will review optimization in 2-space and the calculus concepts associated with it. Learning Objective: After completing this lesson‚ you will be able to model problems described in context and use calculus concepts to find associated maxima and minima using those models. You will be able to justify your results using calculus and interpret your results in real-world contexts. We will begin our review with a problem in which most fixed
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SOLUTIONS TO SUGGESTED PROBLEMS FROM THE TEXT PART 2 3.5 2 3 4 6 15 18 28 34 36 42 43 44 48 49 3.6 1 2 6 12 17 19 23 30 31 34 38 40 43a 45 51 52 1 4 7 8 10 14 17 19 20 21 22 26 r’(θ) = cosθ – sinθ 2 2 cos θ – sin θ = cos2θ z’= -4sin(4θ) -3cos(2 – 3x) 2 cos(tanθ)/cos θ f’(x) = [-sin(sinx)](cosx) -sinθ w’ = (-cosθ)e y’ = cos(cosx + sinx)(cosx – sinx) 2 T’(θ) = -1 / sin θ x q(x) = e / sin x F(x) = -(1/4)cos(4x) (a) dy/dt = -(4.9π/6)sin(πt/6) (b) indicates the change in depth of water (a) Graph at
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December 2011 Vectors Math is everywhere. No matter which way you look at it‚ it’s there. It is especially present in science. Most people don’t notice it‚ they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH north. It has both magnitude‚(in this case speed) and direction. Vectors have specific
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Martyna Wiacek MTH 116 C- Applied Calculus 11/6/2012 Chapter 5 Writing Assignment There is a correlation between area‚ accumulated change‚ and the definite integral that we have focused on throughout Chapter 5 in Applied Calculus. When looking at one rate-of-change function‚ the accumulated change over an interval and the definite integral are equivalent‚ their values could be positive‚ negative or zero. However‚ the area could never be negative because area is always positive by definition
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1790. They worked on the metric system and supported a decimal base. In 1808 Lagrange was named to the Legion of Honour and Count of the Empire by Napoleon. Lagrange later died in 1813. Lagrange‚ along with Euler and Bernoullis‚ developed the calculus of variations for dealing with mechanics. He was responsible for laying the groundwork for a different way of writing down Newton’s Equation of Motion. This is called Lagrangian Mechanics. It accomplishes the same
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quantity which depends on direction a vector quantity‚ and a quantity which does not depend on direction is called a scalar quantity. Vector quantities have two characteristics‚ a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type‚ you have to compare both the magnitude and the direction. For scalars‚ you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding‚ subtracting‚ multiplying
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