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.

~Finding limit at x=c, you are finding outputs that approach "c", your finding the "y" values of f(x)as x is approaching c. There can be a "hole" or what we call a "Removable Discontinuity", this "hole" can be covered with a piecewise function.
~When plugging in number x=c, there is an exact point. There is no "hole". You are finding the output(y) when x is equal to a constant.
-The two are the same when you take the limit of f(x) as x approaches "c".


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

~Change of Y divided by the change of X is the same when you are finding the slope of either one.

~Finding slope of a derivative involves many complicated equations of how to find tangent and secant lines, using LIMITS/: ,with using equations like that one below.../:


~Finding the slope of a line is easy, all you need to do is find the RISE/RUN...
In other words, find the change of Y over the change of X.

Limits

Sorry for posting this up late Ms.Hwang I thought i had posted it up earlier...(:
oooopppps.(:

At first the sine functions were confusing
but when Ms. Hwang(you) explained to me it was more clear, i thought the limit when x aproaches 0 was the same as when the limit aproaches infinity.
Now i know the difference(:
I wont forget(: lol!

The piecewise functions are a little more challenging because there is more than one equation in the problem, making the problem that much harder.
Those problems are pretty hard and i would apprectiate more help on them(:

Problems i also get stuck with is like #5 on p.95
when the limit aproaches 0.... and it is the denominator.
that confuses me.. with the extended functions....?
Gosh../:
I need help(:
and would appreciate some(:

Colleges.

MAJORS
Three majors I wouls see myself doing would be something like....
1.Becoming an Elemantary School Teacher, preferrably kinder or pre-k, why you ask....
Well I love kids... I love to work with kids. Some may be annoying but over all they are just little and barely learning in this BIG world. I love to be around kids the things they say can make your day. I've been told I do good with kids, my friend told me he would trust his kids with me. (:
I believe in a toddlers first year they need to learn a LOT in order to make it. I may be a big help in helping them.
Some teachers I've been told do not make a lot of money, but if this career makes me happy then so be it... Money doesn't buy happiness, and I enjoy working with kids its fun.

2. Engineering
WOW!!! I never new how many types of engineering there were until I did this assignment. There are so many cool different tpes of engineering but I can not come to choose what I would like to do at this point, I want to see how they work and then I will be able to choose specifically what type of engineer I would like to be.
All I know is I would like to pursue in an engineering road just because they make A LOT of money, My cousin is a college graduate from Berkeley and is pursuing her career in engineering. So I can get help from her.

3. Psychology
I am also not so sure but I would like to help people with their problems.
As a young teen I have learned to deal with stress, family problems, friends, sports, and most important SCHOOL. I am always helping friends, and they come to me seeking for advice I make them feel comfort and show them they have someone to lean on that cares about them.
I feel like if I am able to help at least one person and brigten their days that makes me feel good inside knowing I was the one that helped. (:
So I feel like becoming a psychologist will help me help other people.


COLLEGES
Here are some colleges that have the career I am interested in..

1. For education and becoming a school teacher there are many of thousands of schools to get accepted to. There are literally over 1,100 schools that I can choose from. Counselors, friends, and family have all told me that CSUN has a good child development program. But I prefer to challenge myself and try I would like to attend a school that is harder to get accepted, and accomplish making it n that school. I just don't know where to.

2. To become an engineer good schools include...
UC Berkeley offers good Engineering programs, I would like to attend Berkeley. But to my understanding, Berkeley is one of the most competitive schools. My counselor told me that it is slim for me to get in and its VERY HARD to make it in so she killed my dreams if one day going to Berkeley :( lol, BUT! no matter how much people tell me I wont be able to make it, I DO NOT CARE!
I will try MY BEST to make that dream possible, to accomplish my dream though I have to work EXTRA harder in making that dream possible for myself. I will not give up no matter what happens(:
UC Irvine also has a good engineering program that I perhaps can be interested in achieving.

3. For a pschology career there are many schools as well just depends on the exact career I would like to take...
I know I would like to become a Psychologist but not so sure on what school I would like to attend.
Southwestern College in Arizona has the career one of the careers that I am looking at.

Tips and Hints

1.
What I know about transformations are that when there is a number with x eg. (x+3), the graph goes to the left. If you were to have something like (x-3) the graph would shift 3 units to the right. In the case of the number being outside the parentheses the graph would shift up or down depending on the problem.
Ex.
y=(x+1)-8....
This graph would shift 1 unit to the left and 8 units down.
The only helpful tip I can say about transformations is that if you want to determine if the graph goes to the left or right make the y=0 and just solve for the x and the number.
Like y=(3x+15)-39
0=(3x+15)
0=x+15 minus 15 to both sides
your left with x=-15
When the graph goes up or down that is easier, you just need to look at the positive and negative numbers.

2. Honestly, about trigonometry I can't remember much (I have a horrible memory), but I do remember somewhat of sin, cos, and tan, and there reciprocals. I remember the TRICKY unit circle which I didnt understand in my Trig class, but now in calculus I kearned how to remember the radians and the coordinates, (1/2 , root of 3/2) which is pi/3.
From my Trig class I don't remember much but I do remember some of the graphs...like a parabola, x^3 graph, I now remember how to do asymptotes on the tan graps(:
Other than that I really dont remember much but have learned in calculus all over(:

3. What worries me is inverse like how to find or solve for x. When there are a lot of other numbers in front of it, how to graph the inverses or the sohcahtoa graphs, the more complex graphs.

Logs and Inverses

Hmmmmmm... Well what to say about Logs and Inverses.

There are so many things about these two topics.

Here is something i had a somewhat clear understanding of...

Logarithms: Logs first of all are... logx=10

First of all you would have to know that when there is "no" base or at least you can't see a base the base is 10.

So the problem would be the log base 10(x)=10...which means x equals 1.

ex.

log5(x)=125 making x=3

you can make it easier and say log base 5(x)=5^3, and that makes x=3.

ex.

log(xy)= log x + log y

Logs can also be described as natural log.

ex.

ln(x)=x, when the input equals 0.

Where is the base you ask..? the base is like in logs its invisible but its still there except for natural logs the base is "e"; "e" is a number like pi, which equals about 2.718.

-An exponential function is a function where we know the base and need to find out the exponent.

ex.

y=3^x

For this problem you would have to know what the x equals to find the outputs, the inputs are essy to find just plug in any number for x.

-A power function is a function where the x is the base.

ex.

y=x^2

y=x^3

I had a clearer understanding of inverses.

-An inverse is the same as an f(x) function but its f^-1(x).

For f(x) the input is x and the output =y.

For the inverse of f(x) the output would be considered the x and the input would equal the y.

They basically switch.

For an inverse to be a "one-to-one" it has to pass some tests.

The parent fucntion has to pass the vertical line test, and horizontal line test for the inverse to be a "one-to-one" function.

Some things I need help with is the same as most of my classmates...

how do we graph without the use of a calculator.

And the more complicated log functions...?

Odd and Even Functions

Sorry for the delay on posting my blog Ms. Hwang, I had a few problems.

At first when Ms. Hwang tried to explain the odd and even functions I was confused,

but after reading throught pretty much everyones blog I know have a better

understanding about even and odd functions.

An Even Function to my best understanding is a function which is symetrical to the y-axis.

An even function should create a mirror like shape on the quadrant number 1 as created on quadrant number 2.

The equation of an even function should look something like this, f(x)=f(-x).

ODD FUNCTION: To my understanding of an odd function is that the function

is symmetrical to the origin. The equation used to find the odd function is -f(x)=f(-x). Odd functions pass through the x-axis and through the y-axis.
Remains the same as the origin but is reflected over to the x-axis as well as the y-axis.

About Me

Hello there.

My name is Jessica Ivette Carrillo, I am 16 years old.

My birthday is September 24, 1993. My favorite color is PURPLE!! :)

I enjoy playing soccer, running, being with friends, and ICE CREAM!!!

I love Cold Stones ice creams it is the best!

I like to watch movies, scary movies are fun!

I like playing soccer outside with my neighbors and friends,

although my street is the "Bad Luck" Street, thats what my friends

call it, I broke my foot, my friend injured her ankle, my neighbor injured

her foot as well, and just yesterday my front door neighbor fell and hurt his

wrist. Many other things have happened but never too serious, my neighborhood

is a lot of fun. Well thats all I have to say for now, so any more questions just ask me :)