Infinitesimal calculus

1. What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number? Answer: If the equation is 7th degree then it has 7 roots. Those roots can be complex or real. Complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one. This in other words, if one complex root is a + bi, then the other complex root is a – bi. If at least one root were complex, then we would have a…

Semra Özal CONNECTIONS OF LOGARITHMIC FUNCTIONS Logarithm and exponential functions have close relationship and they are inverse function of each other in a way. Before explicitly clarifying this inverse relationship, we should analyze their definitions. Logarithm means, in mathematics, “The exponent that indicates the power to which a base number is raised to produce a given number “2 Exponential function means that “mathematical function in which an…

PBL Blended Career Activity Mathematician Individual Group Work: Description of Career: Mathematicians conduct research to develop their understanding of mathematical principles, and through this, they can apply mathematical techniques to everyday world problems in order to come up with alternative ways to solve those problems which eventually lead to a new solution that can possibly benefit you and the world around you. Mathematics are used everyday, no matter the career, whether it be in…

This year I decided to challenge myself academically. I made the decision of taking four AP classes and math analysis so, to say the least it has been a difficult journey. In addition, out of all the classes I took I struggled the most with AP Chemistry. The material is pretty difficult to understand, even after spending a couple hours to review my notes some things would still be a little blurry. I was failing my test. I was failing my quizzes. I was failing at everything. It was a pretty…

The Philadelphia 76ers trend is upward sloped, and attendance increased as the Sixers win percentage went up. From 1994 to 2013 for the most part there wasn’t much divergence from the line of best fit expect for in the years 2001 and 2003. In the year 2001 the divergence is extreme; based on the line of best fit, one would expect approximately 80 % attendance for a 52% win rate, however this was not the case. In 2001 the attendance was at the Sixers highest between the years of 1994-2013 at…

One challenge I've experienced during my pursuit in engineering and my education as a whole has been AP Calculus AB. Considering I've had high grades in previous maths, I assumed that calculus would not be a problem. However, those previous classes could not have given me a sense of what a college level math class would be like, which I learned very quickly. Calculus has been a surprising taste of what college learning is like. I now know that much of the learning is going to be one's own…

I will be going to Pinnacle High school next year, even though I live in the Horizon High School area. I believe I should be registered for the following math class next year, Honors Geometry. In my eyes, I feel this is the best choice for me because I have earned all of the necessary requirements. So far this year I have maintained a 4.0 G.P.A in all of my classes including Algebra. I also have successfully gotten an 86.20% which passes the 80% needed to pass the final. Now with the grades that…

In this paper, I will argue that John Stuart Mill’s, act-utilitarianism (AU), does not fulfill the complexities of a person’s virtues and the influence it has on their motives. AU claims that an action is right if it brings the greatest amount of happiness for the general well-being. Furthermore, Mill believes that the concept of morality contains two of the main utilities in the Greatest Happiness Principle: a person’s actions are right in proportion as they tend to promote happiness; wrong as…

of pleasure, from the decisions of the administration. The administration uses Parade Day as a way to not claim responsibility for the actions of the students, and to avoid the repercussions of their actions, by closing down the campus. Hedonistic Calculus, which is a tool to calculate whether an action is pleasurable or painful, does not only take the students into consideration, but as well the…

The Calculus Controversy is a very famous argument among many mathematicians. This argument consists of one simple question: who invented calculus? Many mathematicians argue Isaac Newton invented calculus; others say it was Gottfried Leibniz. Let’s start with Isaac Newton. Isaac Newton attended the University of Cambridge. In 1666 he was sent home due to a plague, thus resulting in free time on his own. Because of this, he came up with what we know now as calculus. Newton didn’t call it…