Calculus Magic

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?

limit : When finding the limit of a function at x = c you are looking at numbers going closer and closer to the Consent number at the value of x. Finding the limit of a function at x=c is like a fortune teller trying to predict where the limit will be at.?

Plugging in the number: Plugging in a number into a function is solving the problem and finding the inputs and outputs of a function. Putting constant numbers into a function allows you to graph and find the inverses + inputs/outputs?

The two "magic's" are the same when the limit of X is heading towards constant? :O

2What are the SIMILARITIES between finding the derivativeand finding the slope of a line? What are the DIFFERENCES between the two?

They have the same slope. A derivative of a line is different because it is the slope of the tangent line of a line , whereas a line is a slope of itself..

LIMIT QUESTIONS

1) lim x -> 0 1/2+x - 1/2 / x

2) Any problem involving "Int"

lim -> 2- int x

3)lim x-> 0 sin x / 2x^2 - x

Colleges

1)

• Computer Science : learn how to create programs and develop communication with computers. Desgin websites and learn how society interacts with computers.
• Computer hardware engineering : Learn how to combine math and sience and create and design new designs for computers.
• Computer Programmer: Occasionally use java and html codes. Learns how to use the computer language and work as an individual or in teams. Master most of the scripts and test for use in society.

2)

• Csun : A 4 year university, offers bachelors and masters , large and popular
• USC Davis : great environment , motivated students , 4 year , offers same as UCLA
• UCLA : Well known school , great environment , 4 years, offers masters and bachelors. Motivated students.

TIPS AND HINTS

1) for transformations I always try to remember the original graph. I look at numbers that are included and look for any negitives to flip a graph over. Remembering the unit circle and parent graphs of trig functions help. Numbers with X stretches graphs Horizontally

2) To me , trig are involved in the unit circle. Almost everything is related to the circle.

Sin 3(2X)

The 3 makes the amp go up

2 makes the sin graph more together.

3) Relating the unit circle with functions. Graphing trig functions

Logs and Inverses

1) Logs

• The inverse of B^x
• All Logarithm functions pass through (1,0) because anything to the power of 0 is 1

2)Inverses

• The equation for Inverses is f(x)= f^-1(x)
• the Output and the input change positions. Y is X and X is Y
• Symmetrical on a graph with the original function on the Y=X line
• Slope is consistent between the symmetrical functions.
• Not all functions have inverses.

Things I do not understand

• When using Ln or Log do you always (exponiate) (spelling error )the previous equation?
• Does Log X always have to be the same on the other side of the equation ?
• What are some things to eliminate before attempting to solve the Log function ?

Asian Genital ?

MALE GENITAL ?

People often make a joke out of an asian males genitals.

Saying things like " hahaha yours is small" or something like that often offends us , But it doesn't offend me.

Asians are just like black and white people. Whether it be a size 20 or a 2 inch.

It depends on your genes people!

But ill admit mines small ,and am not afraid to say it

but its NICE.

I have quality and balance down there people.

Besides if a girl came up to me and said my genital was small , Id say that shes probably too loose down there anyways.

EVEN and ODD functions

Even Functions :

For even functions the input for an even function is always opposite from the each other. Speaking Mathematically f(-x)=f(x) for even functions. However graphically its just a reflection of a even functions. Even functions are always symmetrical on the Y-axis. When an input is placed ;the Y-axis always stays the same,but the x intercept is opposite from each other. The parent function of X^2 is a perfect example to portray this explanation since placing a input gives you one output.. Which I like to think of as (X,Y)As you can see in the picture, the X-intercept is opposite of each other and the Y-intercept in Quadrant 1 is the same in #2. The Y-intercept is symmetrical.

ODD Functions : Speaking Mathematically a Odd function is defined as f(-x)=-f(x). Odd functions are always symmetrical about the origin. Simply put , an even function are opposites of each other like the even function however contain different points. A line is a perfect example to portray an Odd function. Since a line is on the origin and reflects the output as symmetrical points on the graph.As you can see, the line is reflecting on the origin and the points on Quadrant 2 and 3 and the opposite of each other. (X,Y) on Quadrant 2 are all positive , Whereas Quadrant 3 (X,Y) are all negative.

( I GOT THE LINE GRAPH IDEA FROM A FELLOW STUDENT. )