To the incoming Math Analysis students, to make sure that you have a fun
and successful year you must be responsible. This is your
responsibility because it was either your own choice or your parents'
that you are taking this class the following year. This class is a rigorous and difficult course, however it is easy if you follow instructions and complete your required assignments on time and legitimately. Do not procrastinate otherwise you will be left behind and clueless when you enter the classroom the next day. Be sure to ask plenty of questions if you are confused about something! Remember it is not bothersome to ask the teacher, they are there to help you.
Adjusting to the flipped classroom can be confusing at first. You will make several accounts, most likely Edmodo, Mentormob, and a Blogger Be sure to keep track of Edmodo as you will receive important updates for class assignments. There will be instructions on how to use and upload the assignments.
The Flipped Classroom is an ongoing experiment. Instead of learning in the classroom you will have time at home to watch tutorials on the concept you are learning about and upon the next day you will be expected to have watched the video(s), be exposed to the material, and have questions on what you have trouble on. Good Luck and Have Fun~
1. Unit V “Big Questions” Blog Post - 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). Your post must include text and some form of media (picture/video) to support your writing.
The Difference Quotient can be explained as we are attempting to find the tangent line in a function on a graph. First we will have a curved line that has a secant line that will touch the graph twice and a tangent line that will only touch it once. At the farthest point of intersection, we will use dx to solve for the secant line and labeling it as h. As we see that the secant line is no where near the tangent line, the equation is f(x+dx)-f(x)/dx. We need to find the value for the secant line that is closer to the tangent line. We can make dx smaller so that the secant line is barely touching the tangent line. The slope of the secant line can be described as the difference quotient, we can find the slope by using the slope formula which is m=y2-y1/x2-x1. Then we can plug in the x-value (x+h)and then the y-value (f(x+h)) the new equation would be (f(x+h)-f(x))/(x+h)-x)). As we simplify this function we see that f(x+h)-f(x) does not simplify. Then we use lim-->0 to show that the secant line and the tangent line cannot touch.
Here is an example of how the difference quotient turns out to be, A being the tangent and B the secant:
Unit U Big Questions
1) What is a Continuity? What is a Discontinuity?
A Continuity is a graph that can be drawn without having to lift your pencil off the paper, meaning that the graph will have no holes, jumps, or breaks within the line. While a discontinuity is a graph that will have breaks, holes, and/or jumps within the graph.
Continuity Graph:
Discontinuity Graph:
2) What is a limit? When does a limit exist? 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, it exists when the line on the graph from the left or right meets up in the same place.and the same value of x and has no discontinuity whatsoever. Limits exist only when there are discontinuities, the difference between a limit and a value is that the value is an exact answer while the limit is just a notation explaining the discontinuity on the graph.
Example of Values:
Example of a Limit:
3) How do we evaluate limits numerically, graphically, and algebraically?
We can evaluate a limit numerically by making a chart which represents our x-values F(x). We then write our limit statement: lim-->x f(x)=x while subbing the x when necessary. We can evaluate the limit graphically by looking at the graph to check and see if there are any points of discontinuity, if there are no points of discontinuity then the graph will have no limits. We can solve a limit algebraically by substituting x from our limit statement to our functions. There are a total of 4 different answers that we can receive from doing this: A number, 0, undefined (DNE), and 0/0 which means that it cannot be found there. This means that you will have to multiply the conjugate to get rid of the 0 in the denominator and simplify, then start from there again.
