TAILIEUCHUNG - Mathematics - Lecture 17: Zeros of polynomials inverse functions

Mathematics - Lecture 17 "Zeros of polynomials inverse functions". The main contents of the chapter consist of the following: Rational zero test, inverse functions, one-to-one functions, restriction of domain. | Zeros of Polynomials Inverse Functions Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 17 Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 1 / 61 Outline 1 Rational Zero Test 2 Inverse Functions 3 One-to-One Functions Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 2 / 61 Rational Zero Test Theorem Given a polynomial p(x) = an xn + an−1 xn−1 + · · · + a1 x + a0 with only integer coefficients and an = 0, if p , a fraction in lowest terms, is a zero of P (x), then p is a factor of a0 q and q is a factor of an . Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 3 / 61 Remarks: 1 The Rational Zero Test gives a finite set of “candidate” rational zeros. Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 4 / 61 Remarks: 1 The Rational Zero Test gives a finite set of “candidate” rational zeros. 2 The Rational Zero Test does not give all the zeros of the polynomial, as polynomials may have irrational zeros, Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 4 / .

• Toán học
• Lecture Mathematics
• Polynomials inverse
• Polynomials inverse functions
• Rational zero test
• Inverse functions
• One to one functions
• Lecture Business mathematics
• Bài giảng Toán kinh doanh
• Business mathematics
• Financial mathematics
• Net present value
• Internal rate of return
• Mathematics 53
• Lecture Mathematics 53
• Integrals yielding logarithmic
• Exponential functions
• Integrals of exponential functions
• Natural logarithmic function
• Inverse circular functions
• Integrals yielding
• Derivatives of inverse circular functions
• Graphs of inverse circular functions
• Hyperbolic functions
• Inverse hyperbolic functions
• Derivatives of hyperbolic functions
• Indeterminate forms
• L’Hôpital’s rule
• Polynomial functions
• Basic types of functions
• Constant functions
• Linear functions
• Limit of a function
• One sided limits
• Limit theorems
• One sided limit
• Infinite limits
• The greatest integer function
• Vertical asymptotes
• Infinity formal definition
• Intuitive definition
• Horizontal asymptotes
• Continuity of functions
• Continuity on an interval
• Essential discontinuity
• The intermediate value theorem
• The squeeze theorem
• Trigonometric functions
• Continuity of trigonometric functions
• Differentiation rules
• The tangent line
• Definition of the derivative
• The chain rule
• Chain rule theorem
• Funtion theorem
• Geometric interpretation of differentiability
• Higher order derivatives
• Implicit differentiation
• Local linear approximation
• Rates of change
• Rectilinear motion
• Position function
• Instantaneous velocity
• Related rates
• Function of time
• Problem on related rates
• Numerical facts
• Mean value theorem
• Relative extrema
• Critical numbers
• Decreasing functions
• The second derivative test
• Points of inflection
• Graphing polynomials
• Second derivative
• Graphing functions
• Vertical asymptotes
• Oblique asymptotes
• Absolute extrema
• Bounded intervals
• One relative extremum
• Absolute maximum
• Optimization word problems
• Optimization problems
• Solving optimization problems
• Integration by substitution
• Theorems on antidifferentiation
• Substitution rule
• Particular antiderivatives
• Application to rectilinear motion
• Plane region
• The definite integral
• Properties of the definite integral
• General antiderivative
• The second fundamental theorem of calculus
• Arc length
• Area of a plane region
• Horizontal rectangles