When Sir Isaac Newton was among other things, the drafting of the orbits of the planets in 1600, he realized that the mathematics of the day were simply well-to-easy. So he invented a new branch of mathematics called calculus. What was different about this new math was that allowed to help you deal with "infinite", or extremely small amounts. In fact, based on these mathematical infinitesimal able to calculate things like the exact speed of a moving bodya particular moment in time, or the exact area of an irregularly shaped strangely. The border is one of the most important calculation that can do extraordinary things about this.
Led to the Age of Enlightenment on the back of the giants as Isaac Newton, Adam Smith and Charles-Louis de Montesquieu, the calculation could not be about for a long time to come are both cradle and maintain the scientific revolution. This new math used once, the world would not be the same:Movement of planetary bodies and the law of universal gravitation could now be adequately explained. Newtonian physics would have been a stronghold for the next 300 years before Einstein would be the new world of relativity theory to explain the corrections to the movement at the speed of light. And all this capacity and because the discovery of something as fundamental as the concept of the border. What this intriguing concept, anyway?
If you think that the dictionary definition ofLimit is reached when something, or something that serves as an absolute limit or extreme, then you get a good idea of what is the mathematical definition as well. Of thinking, while Newton's time, that this simple concept could herald a new era of scientific thought would be measured at best. However, a new era of thinking exactly what we got. You see the border allows us to something like the derivative is calculated, and this idea is what drives essentially allCalculation, which has as its sub-sectors of the differential calculus and integral calculus. Of these branches, the mathematical nature of the whole spacecraft with instruments such as ordinary and partial differential equations, indefinite integrals and definite, and where they are no longer sufficient, other instruments such as the power series and Lagrange multipliers.
To understand intuitively the border, let's look at look like the following mathematical expression as a function: y = 1 / x. This means thatdependent variable y is equal to one independent variable x. The common values of y are the values that we allow them to proceed given x. So, if x = 10, then y = 1 / 10 If x = 100 y = 1 / 100 and so on. The limit is a function value is reached when the independent variable, in this case, x gets closer and closer, not necessarily the equivalent, a different value.
For example, if y = 1 / x, if we examine what happens to y as x gets closer and closer to 2,We will see that the value of the function y is closer to ½. We can do this by going to x = 2.01, then 2,001, then 2.0001, and calculation of the value of 1 / x or y. For each of these values, we get y = 0.4975, then y = 0.49975, y = 0.499975. Note that the x gets closer and closer to 2, then y closer to ½ or 0.5 gets.
Now you can say: "What is the problem that is so obvious?" But there are times when the outcome is not clearall. This is the interesting moment, and if we need some very clever tools to find out what the limit actually is. The border also helps us on things that are mathematically impossible to do, to speak. For example, they learned that you can never divide by zero, and that everything has been divided by zero is undefined. But the concept of the border allows us to talk about this thing. How?
Take the function that we used in this article, y = 1 / x. We can not allow that x = 0, since we cannever calculate the value of y. But now with the concept of the border, we ask, "What is the limit of y as x approaches 0?" If the same x values, closer to 0, we have performed, you will begin to see exactly what happens to y. You can then create a good tip, what happens to y when x approaches zero. At this point we entered a new realm, or should we say, dimension: that of the infinite. And in this context, a lot of strange things beautiful. Occur
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