Algebra vs Calculus

Finding the limit of a constant and the output of a constant.

• Fnding the limit of f(x) as x->c could have two different ouputs.

For exapmle: the function f(x)=x/absolute value x the limits as x->0+ side equals 1.

and as the limit as x->0- equals -1. however

• Plugging in the constant will only give you one output.

When just plugging the number 0 it gives you only one output. In this case however there is no output for f(0).

• These two cases could be the same when the limit as x approaches the constant and when just plugging in the constant are equal.

For example: the function f(x)= x^2

The limit as any constant from both the positive side will give you one output.this goes with plugging in the constant too because it gives you the same output.

basically: limit x->c+ f(x)=limit x->c- f(x)=f(c)

Difference between slope of the line and the derivitave.

• The slope of the line.

The slope of line only determines the slope for that single point.

• Derivitave

The derivitave gives you the formula to find the slope for function to every direction of the function so the function must be continuous.

• They are similiar because the give the dx/dy for the given point.

i have reached my limit...

what i dont get about limits

-one thing i don't get about limits is when to plug it it. because occasionally you have to solve first then you can plug it in. what makes it right to solve first then plug it in until it cannot simplify any longer???

ex: lim 1/2+x-1/2/x

x-->

to solve first you ave to find the least common demonator for the fractioned numerator but why cant you just

what i do get.

2. the limit of a constant will always give you that constant as the answer.

3. you can occasionally brake limits apart. that can make it easier because you ccan then find the limit for the separate equations.

COLLEGE and MAJORS

3 Majors:

1.Computer science- majors learn about computer systems and the way humans and computers interact from a scientific perspective. Instruction includes the theory and design of hardware and software.

2.Computer engineering- majors learn to analyze, design, and develop computer hardware and software.

3. Civil engineering- majors learn how to use math and science to design big construction projects. Topics covered include the calculation of how much weight a structure will hold and the environmental issues that surround construction.

3 Colleges:

1. UCLA.

admitted 23% applicants accepted not easy but possible.

2. POLY POMONA.

admitted 53% applicants accepted not an easy chance but possible.

3. UC BERKELEY.

admitted 22% applicants accepted very not easy but possible as well.

?TIPS AND HINTS?

1.Transformation?

first thing that comes to my mind when i hear transformation, same graph just sabotaged. this helps you know that the x is still itself and whatever is being added or subtracted to the input means it either shifts to the left or right about the x-axis. + to the left - to the right. and then more sabotaging...when the output is either added or subtracted to the graph moves either up or down about the y-axis. + up - down.

2. trigonometry?

hmmm...first relate trigonometry to every type of math you have taken in your life smashed together in some sort of frenzy. basically the relations between sides and angles not only using geometry but algebra as well. estimations , add, subtract, multiply, divide, you name it. it will be found in trig. as long you get those bases down you be fine and apply them to solve for every type of arithmetic.

3. what confuses me?!

what can i start with okay everything confuses me. one topic which we have been working on i am having difficulties to fully understand. inverses! logs! they seem to make sense but i still forget how to separate them when they can be and when its a function and when it is not a function.

Logs and Inverses?

LOGARITHMS

being honest. i didn't really understand much in this section however.

log. the power that a base # must be raised to in order to equal the given number.

one way you can remember. is that the base is always in the bottom because its the base.

and the number given will always be number next to the bottom number. now what goes after the = sign?

this is the number that the base (the bottom #) must be raised to in order to give you the given value.

know also that logs are functions so they need number an (x) forsay otherwise it doesnt exist because a function cant just be itself.

if there is easier ways to remember please feel free to share.

INVERSES

even and odd functions

EVEN:

an even function is when f(x) & f (-x) are equal. and they are symmetrical of the y-axis.

here is one example: f(x)= 3x^4+2x^2

well lets replace them and see...

f(-x)=3(-x)^4 + 2(-x)^2 simplifies to

= 3x^4 + 2x^2

and you then can determine that f(x) is in fact equal to f(-x).

plug in 1 and -1 one they will come out on the same horizontal line.

ODD:

now odd functions are different they are symmetrical about the origin. basically 180 degree turn.

however its the -f(x) is equal to f(-x)

example: f(x)= x^3-4x

f(-x)=(-x)^3 - 4(-x)

= -x^3 + 4x factor out the 1

= -(X^3 - 4X)

finally you can determine that f(-x) is equal to -f(x).

(note: i have not fully understood every concept to even and odd functions so,

i am accepting any type critique and/or comment pertaining to even and odd functions).

thanks.

about me

hello my name is william corcio. i am 16 and currently a junior at john h. francis polytechnic high school or something of the other. many of my friends and all my family members know me as Levi. i love skateboarding and i love arithmetics. i like going out the movies and spending time with friends and family members. i defintely would like to get thru this course so i will need lots of help. i attend TFC (TEENS FO CHRIST note: every friday during lunch rm.23) above all i love God. =) comment me!