Core 4 Integrating Trigonometric Functions 2
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This document contains math problems involving trigonometric integration. It asks to: 1) Find the volume formed by rotating y=sin(x) from x=0 to x= about the x-axis. 2) Express cos2(x) in terms of cos(2x). 3) Find the area under y=sin(x) from x=0 to x=. 4) Evaluate the integral of sec2(x) dx.
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This document discusses identifying the domain and range of functions using function notation. It defines domain as the set of x-values and range as the set of y-values. Examples are given of functions, including f(x) = 2x - 10 and g(x) = 3/(x-2). Students are asked to find the domain, range, and values of A, B, and C using the information given about two functions f and g.Core 4 Partial Fractions 4
Core 4 Partial Fractions 4davidmiles100
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This document provides instructions and questions for exercises involving finding the series expansion of rational functions. It references textbook exercises from page 301 questions 7 and 8, as well as additional exercises from page 311 questions 16 and 17, focusing on rational functions and their series expansions.Core 4 Partial Fractions 3
Core 4 Partial Fractions 3davidmiles100
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This document provides instructions and questions for exercises involving using partial fractions to integrate rational functions. It lists the steps to take, then provides 3 questions from the C4 Textbook involving using partial fractions to integrate rational functions from pages 301 and 305.Core 4 Partial Fractions 2
Core 4 Partial Fractions 2davidmiles100
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This document discusses how to find the partial fractions of a rational function when there is a repeated factor in the denominator. When there is a repeated factor, the partial fractions take on a specific form. It lists examples from the textbook to practice decomposing rational functions with repeated factors in the denominator into partial fractions.Core 4 Partial Fractions 1
Core 4 Partial Fractions 1davidmiles100
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This document provides instructions for decomposing rational functions into partial fractions when there are no repeated factors. It lists the objective of finding partial fractions of simple rational functions and explains that without repeated factors, a rational function can be written as a sum of partial fractions. It then directs the reader to specific textbook questions to practice this technique.Core 4 Parametric Equations 2
Core 4 Parametric Equations 2davidmiles100
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The document provides examples of using differentiation to find the tangents and normals to curves defined parametrically. It gives several examples of finding the equations of tangents and normals to curves at given points. It also considers a parametric curve defined by equations y = at^2 + bt + 1 and x = t + c, and shows that given values for any two of the parameters a, b, c, d, and e, the remaining parameters can be determined, resulting in two possible solutions for c.Core 4 Parametric Equations 1
Core 4 Parametric Equations 1davidmiles100
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This mathematics document discusses converting between parametric and Cartesian forms of curves. It contains exercises from a textbook that ask students to describe curves using parameters and to convert parametric equations into Cartesian coordinate equations. The objectives are to use parameters to describe curves and change parametric equations into standard Cartesian x-y coordinate form.Core 4 Logarithmic Integration
Core 4 Logarithmic Integrationdavidmiles100
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This document provides examples and questions to practice evaluating logarithmic integrals of the form (log(x))/x dx. It includes two questions from a textbook exercise on page 235 to work through that involve logarithmic integration. The objective is to recognize integrals that can be evaluated using properties of logarithms.Core 4 Integration By Parts 2
Core 4 Integration By Parts 2davidmiles100
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This document provides instructions for solving a solid of revolution problem using double integration by parts. Students are asked to find the volume of the solid created when the area under the curve between x=0 and x=1 is revolved around the x-axis. The document notes that while integration by parts does not seem promising at first, applying it twice can solve the given indefinite integral. It directs students to further exercises applying this technique.Core 4 Implicit Differentiation 1
Core 4 Implicit Differentiation 1davidmiles100
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The document discusses finding the gradient of implicitly defined curves using implicit differentiation. It provides the example curve x^3 + y^3 + x^2 - y = 0, which cannot be written explicitly as y = f(x) or x = f(y). To find the gradient at any point on an implicitly defined curve, the technique of implicit differentiation is used. The document then poses the question of finding the equation of the tangent line to the implicitly defined circle x^2 + y^2 - 6x + 2y - 3 = 0 at the point (1, 2).Recently uploaded (11)
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FIFA World Cup followers worldwide can secure World Cup Tickets through our online platform, eticketing.co. With a user-friendly interface and exclusive deals, fans can effortlessly book Tickets for thrilling FIFA World Cup 2026 matches at discounted prices. Don't miss the chance to witness the world's greatest Football World Cup 2026 event live.
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Learn how professional sports bettors use the concept of returning starters to gain an edge in college football. This presentation breaks down why returning starters matter, how to evaluate their impact by position (especially quarterback and offensive line), and the importance of coaching continuity and scheme fit. Whether you're a casual bettor or a seasoned pro, these insights will help sharpen your handicapping skills especially in the early weeks of the season.
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Market Research looking into ESPN for Full Sail University assignment
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Core 4 Integrating Trigonometric Functions 2
- 1. Starter Show that . Express in terms of cos 2 x .
- 2. Objective: to use identities to integrate trigonometric functions
- 3. Question 1 The curve y = sin x is rotated radians about the x axis. Find the volume of the solid formed between x = 0 and x = .
- 4. Question 2 Evaluate .
- 5. Question 3 Find the area under the graph of between x = 0 and .
- 6. Question 4 Evaluate .
- 7. Core 3 & 4 Textbook Exercise 1C Page 219 Questions 4, 5, 8 and 9