Algebra vs. Calculus

1. What is the DIFFERENCE between finding the limit of a function at x=c and actually plugging in the number x=c? When are the two cases the SAME?

Difference: when function is discontinuous

(eg.removable discontinuity at x=c)

Finding the limit of f(x) at x=c is finding the y value as the graph approaches c. Where the function may have a hole at x=c, the limit still exists. But when plugging in the number x=c, the output will ibe the exact y value of the function.

for example.

here, the limit f(x) as x approaches the point of discontinuity (lets call this c) does exist. the limit will be the y value of the open dot. but when plugged in x=c into the equation... the output will become the y value of the closed(black) dot.

Same: they are only the same when the graph of the function is continuous.

2.What are the SIMILARITIES between finding the derivative and finding the slope of a line? What are the DIFFERENCES between the two?

Similarities: find the slope and the derivative both are the change of y/ change of x. The process of finding both the slope and derivative require that you find the secant line first.

Differences: In the finding the derivative, we find the tangent line of the point by finding the secant line (picking two points close by) then bring them closer to x=c (or wherever you are finding the derivative for) this is done with limits.

so basically, finding the derivative is like finding the tangent line at that one exact point; whereas finding the slope, you pick two points .(well thats how i would put it)

Excited about monday. Its going to be funny!!

Limits

oh geez. I forgot. So im late.

hmm limits.

1. I don't get number 3 from the test: lim 6sinx/7x (as x aproaches 0).

I cant plug 0 into x directly because there's still an x in the denominator.

what if i split up the problem and change it to lim 6/7 (as x approaches 0) multiply by lim sinx/x (as x approaches 0).

since lim sinx/x (as x approaches 0) equals to 1. and lim 6/7 equals to 6/7. would my answer simply be 6/7????

2. i didnt get number 14 on the test either.

i redid th problems.. then here are the answers that i got:

a) 1

b) 0

c) 2

3. number 17 b on the test. when it said fin a right end behavior model for f.

the original equation is (x^3 - 2x^2 + 1)/(x^2+3)

so i changed it to (x^3)/(x^2) which becomes x

therefore the right end bahavior model would be just x right???

one more problem is the odd and even.. ugh. i've been getting all odd and evens wrong!!!

i eventually found out when i put the equation on the grapher. and its odd right??

i dont know how to do it without seeing the picture.

majors and colleges

3 Majors

It is kind of cliche that my asian parents would want me to do something or become someone somewhere in the medical field. But after all, it is not what they want, it is my life, its what I want. However, I do pursue interest in the medical field. But i am also artist. and here are my 3 major choices:

1. Pharmacology- they study drugs and what its made of, its sources, how it effects the body, and how its used to treat medical conditions.

2. Anesthesiologist Assistance- they help doctors and nurses provide anesthesia care to patients before, during, and after surgery.

3.Studio Arts - students get to explore and try out new medias that they might like.

3 Colleges

1. University of California: Santa Barbara

Santa Barbara, CA

although located in a suburban setting, it has a large number of under grads, a total of 18,892. because it is a big school. Also not too far from the valley.

2. a college that has an Anesthesiologist Assistance major was not found. however I looked up Surgical Technology and RN, and this is the college that I found most interesting:

Loma Linda University

It is well known for its nursing program, and had a small campus of only 1177 under grads, however, here's the catch.. All LLU programs require previous college credit, thus no first-time freshman applicants accepted. Specific programs are applied to rather than generally to the university. So the idea is go to a community college first then transfer?????

3. University of California: Berkeley

is very famous but very hard to get into. I repeat.. VERY HARD!!! applicants admitted: 22% compared to UCLA's 23%. and you think UCLA is hard to get into huh???

well.. it really depends on the major.

There's a lot more that we've not heard of. This website is very useful.

We often limit ourselves to looking at the well known places. But other places may be good too.

Searching for colleges is kind of fun!!

TIPS AND HINTS

Tips and Hints!

1. How i remember transformation??

what i remember is that what ever is done to "x" (the input) is the other way around. and since its been added or subtracted to the x it moves along the x axis. say you add 4 to x... your graph shifts 4 units left. and say you subtract 4 to x.. your graph moves 4 units to the right.

but when things are added or subtracted from the output.. add means up. subtract means down.

for example.. f(x)= sin (x+π) -2. the graph shifts π to left and moves down 2 units.

2.hmmmm trigonometry is pretty broad.. well i'd say as long as you remember the measurements of the circle then its fine. really.. all the are are just rations. fractions.. whatever. at 30 degrees.. its π/6 simply because 60 degrees is 1/6 of 360. graphing is simple.

example: since we know that sin 0= 0, at x=0, y=0

and sin 90 degrees= 1. then just graph it and the transformation should be simple.

3. what worries me: graphing log takes time for me to do but i understand it now. all i have to do is know my graphs well. again graphing log is still my main concern. and solving log. but i don't think thats considered trigonometry. does it??????

My main advice: study your cards!!!!!!!!

Logarithm and inverses

1. something i understood:

• there can not be an inverse without an original function

• i have learned that in order to find the inverse of a graph, we switch the input and output of the original graph. here's an example:

• f(ƒ⁻¹(x)) = ƒ⁻¹(f(x)) = x
• 
  

2. what i do not understand:

many things that i did not understant

• how to graph log.. uh huh. thats right. not at all.

• i also do not under stand how to find x in a case like this: ln (y-1) - ln 2 = x + ln x

(it is when one x is behind "ln" and one is not. i do not know how to separate that x from ln x and put the x's to one side)

THIS TOPIC IS FRIKIN HARD!!!!

EVEN and ODD Functions

EVEN FUNCTION

A function is even if replacing x with -x does not change the original function.

The graph of an even function is symmetric about the y-axis.

Since f(-x) = f(x); point (x,y) share the same y value as point (-x,y).

example:

*notice points (3,3) and (-3,3) and also note how it is symmetric about the y-axis.

ODD FUNCTION

A function is odd if replacing x with -x results in changing all terms of the original function. The graph of an odd function is symmetric about the origin(0.0).

Since f(-X) = -f(x); point (x,y) lies on the graph only if (-x,-y) lies on the graph.

example:

* Note how it is symmetric about (0,0)

*Figure 5 is an Even Function, Figure 6 is an Odd Function

About Me

Hello.

My name is Wanasanunt On-art; "Wendy" or "Kai". Most people at school know me as Wendy. But honestly, I prefer Kai. Kai is short for "Prakai" in thai meaning sparkly and shiny things; it can also mean spark or lightning.

My nicknames were given to me by my father. Both Wendy and Kai.

But i prefer Kai because it has a nice meaning while Wendy is just an English name since the early 1900s that sounds cute and is certainly easier to pronounce than Wanasanunt. My dad said he liked Peter Pan so that was the start of the name "Wendy Darling."

I am 17 years old. I have a lot of pride in my class of 2011. I am Junior. And also Junior class A-track Vice President. Now you know why I have so much pride. I also have a lot of pride in the Advantage Plus Program. It ticks me off when I hear people say that Magnet is better, I'd turn around and SNAP!!!! I believe that our APP is the best and we accelerate faster than any Magnet student on Campus. But that5's just my opinion. (Which will be soon proven a fact!!!)

I love rainy days the most. Because I love my boots. My boots are comfy. I even wear them on non-rainy days. And rarely on hot summer days. I am obsessed with shoes. Well maybe obsessed might not be the right word to use, but let's put it this way, I like shoes. But at the moment I am just too broke to buy a new pair every week or two.

Although I love rainy days, I do feel that they are quite gloomy and it tends to ruin people's moods. Sunshiny days are nice sometimes. Just SOMETIMES.

I loves swimming in the summer. Dipping my toes into the cold pool. Often too cold. But it's alright.

I love to Sample food!!! A lot of FOOD!!!