tailieunhanh - Mathematics - Lecture 9: Inequalities

Mathematics - Lecture 9 "Inequalities" presents the following content: Inequalities: interval notation, order axioms; solving inequalities involving: polynomials and rational expressions, absolute value. | Inequalities Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 9 Math 17 (UP-IMath) Inequalities Lec 9 1 / 27 Outline 1 Inequalities Interval Notation Order Axioms 2 Solving Inequalities involving: Polynomials and Rational Expressions Absolute Value Math 17 (UP-IMath) Inequalities Lec 9 2 / 27 Inequalities An inequality is a statement saying that one expression is less than or equal to another. 3x − 2 1 Inequalities Lec 9 3 / 27 Inequalities An absolute inequality is an inequality that is true for all permissible values. Example: x2 + 1 ≥ 2x x 2 1−x≤ x+1 Math 17 (UP-IMath) Inequalities Lec 9 4 / 27 A solution to an inequality is a value of the variable that makes the inequality true. The solution set of an inequality is the set of all solutions of the inequality. Example: The solution set of x2 > x is (−∞, 0) ∪ (1, +∞). Math 17 (UP-IMath) Inequalities Lec 9 5 / .

• Toán học
• Lecture Mathematics
• Interval notation
• Order axioms
• Rational expressions
• Absolute value
• Absolute inequality
• Conditional inequality
• 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