The Final.

Dear future math analysis student,

Do not take advantage of the extra freedom that is privileged in this class. Hold this advice above all else. Do you want a successful year? If your answer is no, then you simply cannot have a successful year. Somewhere in the classroom there is a poster that says "If it is important to you, you will find a way." This is possibly the most important lesson in this classroom. Take a step back and forget math for right now. Think about the last time you did something, anything. Now realize that at one point in time, this "something" was exactly what you needed and wanted to do. Now that you understand this, apply it to not just this math class, but to your entire schooling. "What do you want to say to them to help them have the most successful year possible?" Simply, make yourself want the successful year.

Take it from me, if you won't listen to Mrs. Kirch, have an open mind. This is the most practical way to adjust to this classroom. Yes, you might miss the lectures from Mrs. Basu (or whoever was your Algebra 2 teacher), but now you can skip ahead if you understand and not have to sit through those boring minutes. Or probably even more common, you can ask questions without having to feel like you are slowing the rest down. Just always keep in mind that the technology is there to help you, not stop you.

Expect having your homework checked thoroughly. Thoroughly. Expect work that seems to be "extra" or however you want to call it, but above these things, know that they are for your own good. Actually, the the greatest tool will be your opportunity to collaborate on the material. That's really what got me through the year, and now on the last test of the year (calculus material) I received a 91%. DO NOT BE AFRAID TO collaborate.

-Ben Camacho


Any further questions? Consider this video!vvvvvvvv

Unit V: Big Question

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.







A regular positive parabola, a slope is found using m=y(sub2)-y(sub1)/x(sub2)-x(sub1). This is basically what we are doing again, only for a tangent line for a single point. This is important to remember! Two points on the parabola are plotted, the second point must be a tad bit to the right and up of the other. Make sure to label the points. In the original formula, "x sub 1" becomes "x" and "y sub 1" because "f(x). Next we draw a line that connects the points, and call that distance "h". So then it becomes "x+h" and "f(x+h)". Next we plug in the new points. Next we just cancel out the +/- x values and we get the difference quotient, or "derivative".












source: sciencehq.com

Unit U: Big Questions

1.What is continuity? What is discontinuity?


Continuity is a concept in calculus that deals with graphs, it means that there is something that goes on (continues) without being interrupted. Discontinuity is along the same lines, but instead of being continuous, it is interrupted by jumps, holes and breaks in the graph.
<----CONTINUITY


<----DISCONTINUITY





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 graph/function. The limit exists only when the right and left limits are equal. On the other hand, the limit does not exist if the graph has a break (jump, oscillating, infinite discontinuities). The difference between a limit and a value is that the value is the number that belongs and appears in the graph.





3.How do we evaluate limits numerically, graphically, and algebraically?

 Numerically: create a table that has x-values and function of x values, use the number that the limit as x approaches, which is what we will find. Write it mathematically (limx-x>#f(x)=).

Graphically: analyze given graphs. Notice if sides do not meet, a limit does not exist. If the graph has discontinuity, the limit is there. Jumps, oscillating and infinite discontinuities = DNE.

Algebraically: we use direct substitution, dividing out or factoring method, rationalizing/conjugate methods. 

Unit R: Student Problem 1

This problem deals with finding exact values of sums or differences. Be sure to notice which equations are solving for sums and which are solving for differences. For this problem, the sum and differences are the same.

Unit R: Student Problem 2

Unit R: Student Problem #3

Unit T Big Question #4

 

 The Fourth Big Question:

Why do sine and cosine don't have asymptotes, but the other four graphs do?

Sine and cosine do not have asymptotes because of their ratios. Cosine is x over r or x over 1. So when a number is input as X, then the value of the ratio will be that number (because the denominator is 1) even if zero was inputted. The same rule applies for sine, which is y/1. So when a value is inputted for Y, the value of the whole thing will be that number.
So what does all this mean?

Sine and Cosine cannot be undefined in these situations. 

Notice all the other trig functions involve cosine or sine being the denominator, and if they end up equaling to zero, then it makes that certain function undefined and creates an asymptote.