TAILIEUCHUNG - Mathematics - Lecture 8: Equations involving rational expressions, radicals, absolute values, and those in quadratic form

Mathematics - Lecture 8 "Equations involving rational expressions, radicals, absolute values, and those in quadratic form" presents the following content: Rational equations in x, equations involving radicals, equations in quadratic form, equations involving absolute values, solving equations via factoring. | Equations involving Rational Expressions, Radicals, Absolute Values, and those in Quadratic Form Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 8 Math 17 (UP-IMath) Equations Lec 8 1 / 19 Outline 1 Rational Equations in x 2 Equations involving Radicals 3 Equations in Quadratic Form 4 Equations Involving Absolute Values 5 Solving Equations via Factoring Math 17 (UP-IMath) Equations Lec 8 2 / 19 Equations involving Rational Expressions To solve: Math 17 (UP-IMath) Equations Lec 8 3 / 19 Equations involving Rational Expressions To solve: 1 Multiply the LCD to both sides of the equation 2 Solve the equation that arises 3 Drop any of the obtained solutions that make the rational expressions undefined (extraneous solutions). Math 17 (UP-IMath) Equations Lec 8 3 / 19 Example: Solve x+4 x+2 − 2x−3 x−5 = 3x−8 . x2 −3x−10 Solution: Math 17 (UP-IMath) Equations Lec 8 4 / .

• Toán học
• Lecture Mathematics
• Rational expressions
• Absolute values
• Quadratic form
• Rational equations
• Equations involving radicals
• Equations in quadratic form
• 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