Letter to Future Math Analysis Students

1. What do you want to say to them to help them have the most successful year possible?  

To have the most succesful year you must watch the videos when you get home right away, and do all your math homework FIRST. MATH IS A PRIORITY! Also, do all the quizzes and tests that Mrs. Kirch gives you, even though they are extremely tedious. When you do all your work, you will have the best test results. If you do not, your test scores will be below average.

1. How can they best adjust to the flipped classroom and learn to work with all the technology I require of them?  (do you have any specific tips for them or experiences you could share?)

Just follow instructions, and don't question why you are doing it. For example, when you make a blog, make sure to follow the directions as stated. I used to question why we did all these pointless exercises during class and pointless blog posts, but I soon learned that it helped me with not only math but also developed other skills that I could possibly use in my future life. For example, when you make a video it is required that we thoroughly analyze and explain a problem to a fellow classmate. I learned how to talk without being nervous which helped me with my public speaking. Math Analysis does not only teach math, but also teaches good ethics and morals that we need to begin creating in our lives. It is not simply remembering a bunch of methods for a test but to learn how to apply it when we encounter a problem.

1. What can they expect to be different from their previous math classes?

The workload is especially different, and the way it is done is also completely altered. Students will no longer be doing all their work in class, but also work at home. Blog posts and videos will be extremely different from what they did at home last year. In previous math classes, you sit in school and learn about boring lectures, but in Mrs. Kirch's class room, you learn the material at home and go to class and ask all the questions you want about math. Asking a lot of questions will get you to ace the test so ASK QUESTIONS.

Unit V: Big Question

Q: Explain in detail where the formula for the difference quotient comes from now that you know!  Include all appropriate terminology (secant line, tangent line, h/delta x, etc).

First of all we have our graph. In our graph, we can find the distance between two points by finding the slope of the secant line. To find the slope of the secant line, all we must do is plug in y2-y1/x2-x1 which is f(x+h)-f(x)/x+h-x  as you can see we can cancel out stuff in the denominator. If we do so, we would be left with our difference quotient

Unit U: Big Questions

Q1: WHAT IS A CONTINUITY? WHAT IS A DISCONTINUITY?

A continuity is a function that can be drawn as a graph CONTINUOUSLY without anything from stopping it. In simpler terms a continuous graph or function can be drawn without lifting our pencil from the paper because it doesn't have any breaks or jumps in it.

A discontinuity is a break, hole, jump, or whatever in the graph that causes it to be discontinuous. It's easy.

Q2: WHAT IS A LIMIT? WHEN DOES A LIMIT NOT EXIST? WHAT IS THE DIFFERENCE BETWEEN A LIMIT AND A VALUE? 

A limit is the intended height of a function. A graph can approach two different directions, left and right. If the height of a function does not reach in the same place from left or right, that is when the limit does not exist. A limit, is the height that a graph needs to reach, and a value is an actual number that a graph reaches. If a graph reaches a hole, that is a limit but it is not a value.

Q3: HOW DO WE EVALUATE LIMITS NUMERICALLY, GRAPHICALLY, AND ALGEBRAICALLY? 

Numerically, we can do it on a table with the x value on top, and the limit of the function on the bottom. Graphically, we are just looking at a graph as shown above, and from there we can determine the jumps and discontinuities.Algebraically we use direct substitution and plug in whatever x is approaching.

Unit T Big Question 4

Unit T Big Question 3

Unit T Big Question 2

Unit T Big Question 1

BIG QUESTION 1a




 BIG QUESTION 1b