reply to each of the discussion post. each post response should be a minimum of 100 words each.

PLEASE REPLY TO EACH DISCUSSION WITH SIGNIFICANT CONTENT. THERE ARE TWO DISCUSSIONS. DO NOT JUST AGREE WITH THE STUDENT BUT PROVIDE SUPPORTING CONTENT IF YOU AGREE OR DISAGREE. THERE ARE TWO DISCUSSION RESPONSE. PLEASE RESPOND WITH A MINUMUM OF 100 words FOR EACH DISCUSSION.

Tessa Chandler 

Dis2

COLLAPSE

Top of Form

1. What is a composition of functions? What is the difference between the composition and the product of two functions?

The more simple I try to make the statement of a composition function the more complicated it sounds. The composition of a function can be defined as substituting the output of one function with the input of another function.. The best way to show is to give an example.

EX:

…function one…F(x)=x+3

…function two…g(x)=5x the output of g is the input on f(x)

F(g(x))=(5x)+3

 

1. Write a short paragraph about the number e.

1. The number e is an irrational number It has the property of being the base of all logarithms introduced in algebra 101. The e stands for the eulers’ number, named after Leonhard Euler. The standard value of e is a decimal spanning past 15 decimal place values. Its first 11 are as follows 2.71828182818.

 

1. What is common and what is different about arithmetic and geometric sequences?

1. A geometric sequence is found by multiplying the previous term by the constant value, whereas arithmetic sequencing is found by adding a constant term to the previous term. Despite this difference they have a common trait. They both create a pattern that cannot be altered, the sequence is set.

Erica Cha 

Week 2 Erica Cha

COLLAPSE

Top of Form

1. One can think of “composition of functions” as a function that takes in its input as another function. That is, if the function is f(x) = x + 2, the input for this particular function in the case of “composition of functions” can be another function like f(x) = x + 4. In this case, the x + 4 will become the input, producing x + 6 as a result. It is different from the product of two functions in that the two functions are multiplied, in the same level, and neither are inputs of the other. I have taken a course in Computer Science, and there is a concept called Lambda Calculus. Lambda Calculus also deals with functions that take in other functions, and it can be said that Lambda Calculus has a composition of functions as one of its basic operations.

Also, if one puts a function f(x) as input in its inverse function f(x)^-1, the output will be x.

1. The number e refers to Euler’s constant (though the e does not really stand for anything), and it is one of the most important constants. It deals with the rate of change and can be found anywhere in nature that deals with continuous growth like population change. By definition it is (1 + 1/n) ^ n as n approaches infinity, and, as one can clearly see from the formula, it is from calculating computing interest. It is essentially a constant where one would get if he or she were to get interests on one dollar continuously. It is important in Calculus as it is the only constant where its derivative is the same as itself.

2. Arithmetic sequence and geometric sequence are similar in that they both have a predicted rate of change (difference and ratio). Also, they can both be easily defined recursively (you can easily write recursive code in Python). However, they are different in that if the ratio is smaller than 1 in geometric sequence (and it does not oscillate signs), sometimes the sequence approaches certain value.

Bottom of Form

 

Bottom of Form