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what is calculas

Guest May 15, 2017
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 #1
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I've tried to understand it so far, and I have figured out that calculus is using estimates that get closer and closer and closer to something to the point where it makes sense that something might work a certain way.

 

One example: \(\pi = 4(1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \frac{1}{11} + \dots)\) Only after infinite repetitions will you get the answer.

 

Another example: \(\phi = 1 + \frac{1}{1+\frac{1}{1+\frac{1}{1+\dots}}}\) Again, only after infinite repetitions will you get the answer (a.k.a. the golden ratio (can be used to make a "perfect" rectangle that can be divided using a method infinite times constantly getting the same ratio), phi)

helperid1839321  May 15, 2017
 #2
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helperid1839321:

Calculus is not that way but what you say is a part of calculus. Calculus do require you to find something nearer and nearer to some points existing. Calculus is a high-level mathematics branch that divides into 2 main parts: differentiation and integration(or differential calculus and integral calculus.)

 

Differentiation is about the slope of the curve at a certain point that can be calculated as the secant line is closer and closer to the tangent line.

 

Integration is about the area under a curve(In earlier maths you estimate the area of irregular figures using grids, now you use calculus to calculate it, only if you have the formula for plotting the irregular figure.) 

 

They also teach you something called limits when you start calculus. Limit means predict what the expression will approach to when the variable(e.g. x, y, a, t) approaches to something.

 

Example of limits:

\(\displaystyle\lim_{x\rightarrow 3} x^2\)

This means, if x is very close to 3, what does x^2 approach to.

As you can predict, the answer is 3^2 = 9.

There are harder limits. You can either solve it by plotting a graph of the function, or by some rules(more precisely, L'Hopital's rule is a way to solve some hard limits.)

 

Example of differentiation.

\(\dfrac{d}{dx}\ln x\)

This means to find the general formula for the slope of any point on the curve y = ln x.

and it is 1/x, when you learn calculus you know why.

 

Example of integration.

\(\displaystyle\int^{1}_{0}x^2dx\)

This means the area under the curve y=x^2 between x = 0 and x = 1.

And this is 1/3, when you learn calculus you know why.

MaxWong  May 16, 2017

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