TAILIEUCHUNG - Mathematics - Lecture 5: Radical expressions and rational exponents

Mathematics - Lecture 5 "Radical expressions and rational exponents" presents the following content: nth root of anpha, simplification of radical expressions, operations involving radical expressions, rationalizing radical expressions. | Radical Expressions and Rational Exponents Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 5 Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 1 / 23 Outline 1 Radical Expressions nth root of a Simplification of Radical Expressions Operations Involving Radical Expressions Addition and Subtraction of Radical Expressions Multiplication and Division of Radical Expressions Rationalizing Radical Expressions Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 2 / 23 nth root of a Definition Let a, b ∈ R and n ∈ N, n > 1. If bn = a then b is an nth root of a. Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 3 / 23 nth root of a Definition Let a, b ∈ R and n ∈ N, n > 1. If bn = a then b is an nth root of a. Examples: Since both 32 , (−3)2 are equal to 9, then 3 and -3 are second roots or square roots of 9. -4 is a third root or a cube root of -64 since (−4)3 = −64. 2 and -2 are fourth roots of 16 since (−2)4 = (2)4 = 16. Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 3 / 23 Principal nth root of a Definition √ If n ∈ N, n > 1, a ∈ R, the principal nth root of a, denoted n a, is defined as follows: √ If a > 0, then n a is the nth root of a that is positive. √ If a < 0 and n is odd, then n a is the nth root of a that is negative. √ If a is zero, then n 0 = 0. Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 4 / .

• Toán học
• Lecture Mathematics
• Radical expressions
• Rational exponents
• Rationalizing radical expressions
• Simplification of radical expressions
• Simplification of radicals
• 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