0 A Review Of Basic Algebra 1 Equations And Inequalities 2 Functions And Graphs 3 Functions 4 Polynomial And Rational Functions 5 Exponential And Logarithmic Functions 6 Linear Systems 7 Conic Sections And Quadratic Systems 8 Sequences, Series, And Probability Chapter4: Polynomial And Rational Functions
4.1 Quadratic Functions 4.2 Polynomial Functions 4.3 The Remainder And Factor Theorems; Synthetic Division 4.4 Fundamental Theorem Of Algebra And Descartes' Rule Of Signs 4.5 Zeros Of Polynomial Functions 4.6 Rational Functions 4.CR Chapter Review 4.CT Chapter Test Section4.2: Polynomial Functions
Problem 1SC: Determine whether or not the functions are polynomial function. For those that are, state the... Problem 2SC: Find the zeros of each polynomial function. a. f(x)=x3x22x b. f(x)=2x4+2x2 Problem 3SC Problem 4SC Problem 5SC Problem 6SC: Show that P(x)=2x39x2+7x+6 has at least one real zero between 1and0. Problem 1E Problem 2E: Fill in the blanks. Peaks and valleys on a polynomial graph are called _________ points. Problem 3E Problem 4E Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E: Fill in the blanks. If (x+5)3 occurs as a factor of a polynomial function, then the ________ of the... Problem 10E: Fill in the blanks. The graph of a nth degree polynomial function can have at most ________ turning... Problem 11E Problem 12E: Fill in the blanks. If P(x) has real coefficients and P(a) and P(b) have opposite sings, there is at... Problem 13E: Determine whether or not the functions are polynomial functions. For those that are, state the... Problem 14E: Determine whether or not the functions are polynomial functions. For those that are, state the... Problem 15E: Determine whether or not the functions are polynomial functions. For those that are, state the... Problem 16E: Determine whether or not the functions are polynomial functions. For those that are, state the... Problem 17E Problem 18E Problem 19E Problem 20E: Determine whether or not the functions are polynomial functions. For those that are, state the... Problem 21E: Determine whether or not the graph of the functions shown are polynomial functions. Problem 22E Problem 23E Problem 24E Problem 25E: Find the zero of each polynomial function and state the multiplicity of each. State whether the... Problem 26E: Find the zero of each polynomial function and state the multiplicity of each. State whether the... Problem 27E: Find the zero of each polynomial function and state the multiplicity of each. State whether the... Problem 28E: Find the zero of each polynomial function and state the multiplicity of each. State whether the... Problem 29E: Find the zero of each polynomial function and state the multiplicity of each. State whether the... Problem 30E: Find the zero of each polynomial function and state the multiplicity of each. State whether the... Problem 31E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 32E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 33E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 34E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 35E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 36E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 37E: Find the zeros of each polynomial function and state the multiplicity of each. State whether the... Problem 38E Problem 39E Problem 40E Problem 41E: Use the Leading Coefficient Test to determine the end behavior of each polynomial. f(x)=5x7+10x32x Problem 42E Problem 43E Problem 44E Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E: Graph each polynomial function. f(x)=x39x Problem 50E Problem 51E: Graph each polynomial function. f(x)=x34x2 Problem 52E Problem 53E: Graph each polynomial function. f(x)=x3+x2 Problem 54E Problem 55E Problem 56E Problem 57E: Graph each polynomial function. f(x)=x3x24x+4 Problem 58E Problem 59E: Graph each polynomial function. f(x)=x42x2+1 Problem 60E: Graph each polynomial function. f(x)=x45x2+4 Problem 61E: Graph each polynomial function. f(x)=x4+5x24 Problem 62E Problem 63E: Graph each polynomial function. f(x)=x4+6x38x2 Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E: Maximize volume An open box is to be constructed from a piece of cardboard 20 inches by 24 inches by... Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E: Roller coaster A portion of a roller coasters tracks can be modeled by the polynomial function... Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E: Explain why a polynomial function of odd degree must have at least one zero. Problem 96E: What is the purpose of the Intermediate Value Theorem? Problem 97E: Use a graphing calculator to explore the properties of graphs of polynomial function. Write a... Problem 98E: Use a graphing calculator to explore to properties of graphs of polynomial functions. Write a... Problem 99E Problem 100E Problem 101E: Match each polynomial function with its graph shown below. f(x)=(xa)(xb)2(xc) Problem 102E Problem 103E: Match each polynomial function with its graph shown below. g(x)=(xa)2(xb) Problem 104E Problem 105E Problem 106E Problem 96E: What is the purpose of the Intermediate Value Theorem?
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4.2.4 Intro To Real Analysis
Transcribed Image Text: 4. Prove that lim cos(1/x) does not exist but that lim x cos(1/x) = 0.
x→0
x-0
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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