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Learn important math skills at this lifesaver site for free!
Wondering how to study math? Wondering how to have fun with math?
Wondering how to MASTER math tests?
Wondering how you can BEAT math on your own?
It is time to put an end to all those pointless questions the answer is right here, under your nose no, technically, it's in front of it! This website is the ultimate key to CRACK mathematics! Here, you will find texts, exercises, and a unique walkthrough to solving math puzzles! Ideal for test "preps", self learners, and every math student!
HAVE FUN!
A Definitive Guide to Mathematics:
(Skipping is not Recommended)
Course Catalogue:
1. Algebra 2. Geometry 3. Trigonometry 4. Basic Linear Algebra 5. Single Variable Calculus 6. Linear Algebra 7. MultiVariable Calculus 8. Advanced Linear Algebra 9. Mathematical Modelling Further studies and careers include anything that has to do with numbers you can choose to be a wellpaid, wellrespected technical whose work is critical to the development of society and evolution of mankind you can be a financial analyst who makes money by pressing keys on the calculator and making calls you can be a military strategist that helps out with out boys abroad and help them "disroot" insurgents and enjoy FREE SUBWAY (YEAH!) and you can be an actual who is a partner of a gigantic multinational corporation. Of course, you can choose to be a MATHEMATICIAN! And you can push the stakes ahead further for generations after you. In a nutshell, you will be much better off than the hobo in the road corner that can't count from one to ten.

Before you embark on the journey of mathConvince yourself that it is WORTH it. And indeed it is. The following paragraph is to preach the merits of Mathematicism.
Math is the study of the ways of the Lord. It is the language of nature Sure! Everybody'd already tell ya that. And ya don't believe it. Or at least, have some doubts. Doubting is encouraged it makes a good mathematician. Math is fun you think it's not because: 1. You got bogged down by the boggy numbers and calculations! 2. Your brain was rampaged with disconnected theorems. 3. Laziness is your inherited trait. Using this site, you will flip past the calculations and numbers cuz this is what math is about! You will connect the isolated theorems. You will HAVE FUN WITH MATH. 
What is a limit?
The limit of a function f(x), at some value a, is simply, what the value of the function approaches when x gets close to a.
Of course, most of the times, the limit is equal to the value of f(a). (What else would you expect?) Most of the times. There are exceptions. Those exceptions are what make the concept of the limit tricky and timeconsuming. Let's take a moment to think what kind of function would it take to make the limit different from the value of the function.
Of course, polynomial functions who are defined everywhere, like y=x, are easy prey to our mathematical minds. The limits of those functions at any x is equal to the value of the function at that point.
Right. Here, I present a part of the FUNCTION BLACKLIST, whose contents produce messy limits, but sadly, takes up most of the space in calculus tests.
1. Functions who are not defined at a. There is no value at a to talk of.
(e.g. Rational functions with the denominator as zero at the point x=a.)
2. Rational functions whose numerator or denominator appears to march off to infinity. Infinity allows no limit.
3. Functions who vibrate violently around the value a.
4. Functions who approach different values when x gets close to a from the left side and the right side.
Be extra careful when encountered with such functions. The limit might not appear to be what it is.
Of course, most of the times, the limit is equal to the value of f(a). (What else would you expect?) Most of the times. There are exceptions. Those exceptions are what make the concept of the limit tricky and timeconsuming. Let's take a moment to think what kind of function would it take to make the limit different from the value of the function.
Of course, polynomial functions who are defined everywhere, like y=x, are easy prey to our mathematical minds. The limits of those functions at any x is equal to the value of the function at that point.
Right. Here, I present a part of the FUNCTION BLACKLIST, whose contents produce messy limits, but sadly, takes up most of the space in calculus tests.
1. Functions who are not defined at a. There is no value at a to talk of.
(e.g. Rational functions with the denominator as zero at the point x=a.)
2. Rational functions whose numerator or denominator appears to march off to infinity. Infinity allows no limit.
3. Functions who vibrate violently around the value a.
4. Functions who approach different values when x gets close to a from the left side and the right side.
Be extra careful when encountered with such functions. The limit might not appear to be what it is.
THE SECOND FUNDAMENTAL THEOREM OF CALCULUS
This is perhaps the most important thing the Integral Sector of this website contains. So, be sure not to waste it.
Well, we just learned about the First Fundamental Theorem of Calculus, and I remembered kicking a statement up there saying that the Second is the more useful one. This theorem will literally solve all definite integrals. Provided that you can find the indefinite integral of the function.
The second fundamental theorem of calculus goes like this:
Well, we just learned about the First Fundamental Theorem of Calculus, and I remembered kicking a statement up there saying that the Second is the more useful one. This theorem will literally solve all definite integrals. Provided that you can find the indefinite integral of the function.
The second fundamental theorem of calculus goes like this:
Where F(x) is the antiderivative, or indefinite integral of f(x). The proof of this theorem really lies with the first one. You can try on your own. I'll try to put it up in documents for download. But now, let's focus on what this theorem does. After all, in tests and in practice, it's the APPLIANCES of theorems that come into use, not the PROOFS. It's a whole different story for people who strive to be mathematicians, but they probably aren't reading this in the first place, so......
What does this say? First, it does not put any restrictions on the function lying inside the integral signs, nor on its lower bound and upper bound, a and b. This means this identity applies to ALL definite integrals. Secondly, we see this is a simple, simple expression, and it agrees with institution: the constant terms of the antiderivatives cancel, making out a definite number for the definite integral. We can calculate the definite integral with a hand calculator.
Now, an example would be this: integrate y=x, 0<x<1. Of course, some folks would try to find the area using the area of triangles. And I admit for this problem it's simpler. But let's use the definite integral. So, the antiderivative of y=x is y=0.5x^2+C, while C is a constant with any real value. Now, plug in x=1 and x=0 and minus the two expressions. (Note that C conveniently cancel.) You get what you want. The answer should agree with your triangle area.
After you convince yourself of the immaculately power of this theorem, seal it in your mind forever, next to the Chain Rule, Rules of Differentiation, and the next day for the dentist.
What does this say? First, it does not put any restrictions on the function lying inside the integral signs, nor on its lower bound and upper bound, a and b. This means this identity applies to ALL definite integrals. Secondly, we see this is a simple, simple expression, and it agrees with institution: the constant terms of the antiderivatives cancel, making out a definite number for the definite integral. We can calculate the definite integral with a hand calculator.
Now, an example would be this: integrate y=x, 0<x<1. Of course, some folks would try to find the area using the area of triangles. And I admit for this problem it's simpler. But let's use the definite integral. So, the antiderivative of y=x is y=0.5x^2+C, while C is a constant with any real value. Now, plug in x=1 and x=0 and minus the two expressions. (Note that C conveniently cancel.) You get what you want. The answer should agree with your triangle area.
After you convince yourself of the immaculately power of this theorem, seal it in your mind forever, next to the Chain Rule, Rules of Differentiation, and the next day for the dentist.