Question

1. Formulate a series and show a proof by PMI to validate.

2. Give at least one example each on the operations of functions.


3. In at least 50 words; What have you learned in GE4?

Answer 1

Series: 1 + 3 + 5 + 7 + 9 + ...

Proof by PMI:

P: The series starts with 1 and increases by 2 for each consecutive term.

M: The nth term of the series is 2n - 1.

I: The series is an arithmetic series with a common difference of 2.

Operations of functions:

Addition: (f + g)(x) = f(x) + g(x)

Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f + g)(x) = (2x + 1) + (3x - 2) = 5x - 1

Multiplication: (f * g)(x) = f(x) * g(x)

Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f * g)(x) = (2x + 1) * (3x - 2) = 6x^2 - 2x + 3x - 2 = 6x^2 + x - 2

GE4 is a mathematical modeling course, in which I have learned how to use mathematical methods and models to analyze and solve real-world problems. I learned how to use statistical analysis, optimization, and simulation to make predictions and decisions. I also learned how to use various tools and software to create and analyze models. I learned to use mathematical tools to solve problems in different fields such as finance, engineering, and science.