a characterization of finitely monotonic additive function
... satisfying n > ~xk and f(a 1 ) f(a 2 ) < . . . < f(an) . In other words, f(m) is said to be finitely monotonic if, infinitely often, f(m) is non-decreasing on a positive proportion of the integers between 1 and Xk . Let ill denote the class of finitely monotonic functions . Approximately 25 years ag ...
... satisfying n > ~xk and f(a 1 ) f(a 2 ) < . . . < f(an) . In other words, f(m) is said to be finitely monotonic if, infinitely often, f(m) is non-decreasing on a positive proportion of the integers between 1 and Xk . Let ill denote the class of finitely monotonic functions . Approximately 25 years ag ...
Geometric Sequences - Makunja Math
... You should be able to identify if a sequence is geometric Given a geometric sequence, you should be able to determine “a” and “r’. You should be able to determine the “nth term” of a geometric sequence You should be able to apply the “nth term” formula to various problem solving situations ...
... You should be able to identify if a sequence is geometric Given a geometric sequence, you should be able to determine “a” and “r’. You should be able to determine the “nth term” of a geometric sequence You should be able to apply the “nth term” formula to various problem solving situations ...
Full text
... We will prove that the final term of each maximal representation is either F2 or F3 and show the pattern associated with the final terms in the representations of 1, 2, 3, 4, 5, 6, ..., namely: F2, F3i F2> F2, F 3 , F2s ... is a Golden sequence with the term F2 corresponding to a unit and the term ^ ...
... We will prove that the final term of each maximal representation is either F2 or F3 and show the pattern associated with the final terms in the representations of 1, 2, 3, 4, 5, 6, ..., namely: F2, F3i F2> F2, F 3 , F2s ... is a Golden sequence with the term F2 corresponding to a unit and the term ^ ...
Sets and functions
... the domain and range are a part of the information of a function. Note that a function must be defined at all elements of its domain; thus for example the function f (x) = 1/x cannot have domain R without assigning some value to f (0). (This is in contrast to the practice in some calculus courses wh ...
... the domain and range are a part of the information of a function. Note that a function must be defined at all elements of its domain; thus for example the function f (x) = 1/x cannot have domain R without assigning some value to f (0). (This is in contrast to the practice in some calculus courses wh ...
2.4: The Chain Rule
... Example 8: Find the derivative of each trigonometric function. a. y sin 4 3x ...
... Example 8: Find the derivative of each trigonometric function. a. y sin 4 3x ...
College Algebra Chapter 2 Functions and Graphs
... A new job offer in sales promises a base salary of $3000 a month. Once the sales person reaches $50,000 in total sales, he earns his base salary plus a 4.3% commission on all sales of $50,000 or more. Write a piecewisedefined function (in dollars) to model the expected total monthly salary as a func ...
... A new job offer in sales promises a base salary of $3000 a month. Once the sales person reaches $50,000 in total sales, he earns his base salary plus a 4.3% commission on all sales of $50,000 or more. Write a piecewisedefined function (in dollars) to model the expected total monthly salary as a func ...
Set Theory - The Analysis of Data
... Proof. Let An , n 2 N be a collection of countably infinite sets. We can arrange the elements of each An as a sequence that forms the n-row of a table with infinite rows and columns. We refer to the element at the i-row and j-column in that table as Aij . Traversing the table in the following order: ...
... Proof. Let An , n 2 N be a collection of countably infinite sets. We can arrange the elements of each An as a sequence that forms the n-row of a table with infinite rows and columns. We refer to the element at the i-row and j-column in that table as Aij . Traversing the table in the following order: ...
Euler and the Exponential Base e
... Euler and the Exponential Base e In the next generation after Newton, Euler made extensive use of Newton's generalized binomial expansions greatly extending their range and utility. Newton used tables to construct infinite series, but once the method of formation of this series had been made clear E ...
... Euler and the Exponential Base e In the next generation after Newton, Euler made extensive use of Newton's generalized binomial expansions greatly extending their range and utility. Newton used tables to construct infinite series, but once the method of formation of this series had been made clear E ...