🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →

HomeClass Notes1,200,000CA670,000

MATH 1300 Lecture Notes - Lecture 6: Irrational Number, Rational Number, Leonhard Euler

76 views13 pages

cerisegiraffe538

1 Feb 2018

School

York University

Department

Mathematics and Statistics

Course

Professor

Paul Skoufranis

For unlimited access to Class Notes, a Class+ subscription is required.

ashleybishopp2000 and 39542 others unlocked

$MATH 1300 Full Course Notes$

MATH 1300 Full Course Notes

Document Summary

Math 1300 lecture 6 notes - exponential functions, applications of exponential functions and the number e. Introduction: the function fsxd 2 x is called an exponential function because the variable, x, is the exponent. It should not be confused with the power function tsxd x 2, in which the variable is the base. In general, an exponential function is a function of the form fsxd b x where b is a positive constant: let"s recall what this means. If x n, a positive integer, then b n b b n factors. If x 0, then b 0 1, and if x 2n, where n is a positive integer, then b 2n 1 b n. A representation of this graph is shown in figure. In particular, since the irrational number s3 satisfies: and we know what 2 1. 7 and 2 1. 8 mean because 1. 7 and 1. 8 are rational numbers.

Related textbook solutions

Calculus

ISBN: 9781319050733

Single Variable Calculus: Early Transcendentals

4th Edition, 2018

ISBN: 9781337687805

CALCULUS:EARLY TRANSCENDENTALS

ISBN: 9781319050740

Related Documents

MATH 1300 Lecture Notes - Lecture 11: Radian, Graphing Calculator

cerisegiraffe538

MATH 1300 Lecture Notes - Lecture 7: Logarithm, Inverse Function, Cube Root

cerisegiraffe538

MATH 1300 Lecture Notes - Lecture 1: Constant Function, Power Rule

Related Questions

Show transcribed image text

pearmosquito116

Algebra

Complete the sentence below. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. Complete the sentence below. The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and If r is a solution to the equation f(x) = 05 name three additional statements that can be made about f and r assuming f is a polynomial function. Choose the correct answer below. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is an x-intercept of the graph of and x - r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a complex zero of the polynomial function r is an x-intercept of the graph of and x + r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is a y-intercept of the graph of x and x + r is a factor of f. Explain what the notation Km f(x) = -infinity means. x rightarrow infinity Choose the correct answer below. The limit of f(x) as x approaches - infinity equals infinity. The limit of x as f(x) approaches infinity equals - infinity. The limit of f(x) as x approaches infinity equals - infinity. The limit of x as f(x) approaches - infinity equals infinity. Form a polynomial whose zeros and degree are given. Zeros: -7, multiplicity 1; - 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. F(x) = Find the vertical horizontal and oblique asymptotes, if any, for the following rational function.R(x) = 12x / x + 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 64 / x2 - 6x + 8 Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, for the given rational function. Q(x) = 2x2 - 7x - 4 / 3x2 - 7x - 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) There is no vertical asymptote. Analyze the graph of the function. R(x) = x + 14 / x(x + 15) What is the domain of R(x)? {x x 0 andx - 16} {x x 0 andx - 16 andx - 14} {x x 0 and x - 14} All real numbers Analyze the graph of the function. R(x) = 5x + 5 / 4x + 12 What is the domain of R(x)? {x|x 0 and x -3 and x - 1} {x|x -3} {x|x and x - 3} All real numbers Analyze the graph of the function.R(x) = x2 / x2 + x - 56 What is the domain of R(x)? {x|x 7 and x - 8} {x|x 0,x -1, and x 8} {x|x 0, x 7, and x - 8} All real numbers

Show transcribed image text Complete the sentence below. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. If r is a real zero of even multiplicity of a function f then the graph of f the x-axis at r. Complete the sentence below. The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and The graphs of power functions of the form f(x) = x n: where n is an even integer, always contain the points and If r is a solution to the equation f(x) = 05 name three additional statements that can be made about f and r assuming f is a polynomial function. Choose the correct answer below. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is an x-intercept of the graph of and x - r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a complex zero of the polynomial function r is an x-intercept of the graph of and x + r is a factor of f. If r is a solution to the equation f(x) = 0, then r is a real zero of the polynomial function r is a y-intercept of the graph of x and x + r is a factor of f. Explain what the notation Km f(x) = -infinity means. x rightarrow infinity Choose the correct answer below. The limit of f(x) as x approaches - infinity equals infinity. The limit of x as f(x) approaches infinity equals - infinity. The limit of f(x) as x approaches infinity equals - infinity. The limit of x as f(x) approaches - infinity equals infinity. Form a polynomial whose zeros and degree are given. Zeros: -7, multiplicity 1; - 3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. F(x) = Find the vertical horizontal and oblique asymptotes, if any, for the following rational function.R(x) = 12x / x + 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 64 / x2 - 6x + 8 Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the vertical, horizontal and oblique asymptotes, if any, for the given rational function. Q(x) = 2x2 - 7x - 4 / 3x2 - 7x - 20 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) There is no vertical asymptote. Analyze the graph of the function. R(x) = x + 14 / x(x + 15) What is the domain of R(x)? {x x 0 andx - 16} {x x 0 andx - 16 andx - 14} {x x 0 and x - 14} All real numbers Analyze the graph of the function. R(x) = 5x + 5 / 4x + 12 What is the domain of R(x)? {x|x 0 and x -3 and x - 1} {x|x -3} {x|x and x - 3} All real numbers Analyze the graph of the function.R(x) = x2 / x2 + x - 56 What is the domain of R(x)? {x|x 7 and x - 8} {x|x 0,x -1, and x 8} {x|x 0, x 7, and x - 8} All real numbers

indigosardine988