Litle help understanding the point behind Calculus .

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sponsoredwalk said:
[tex]Average = \frac{1}{calculus \ - \ precalculus} \int_{precalculus}^{calculus} {(Undergraduate \ Course)}\,d(math)[/tex]

:biggrin:
Hides before being banned
on grounds of FAIL status​


(flagged as AWESOME)

p.s. what is the "Hides before being banned..." about?
 
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The value of many things learned in mathematics may be clear only later on when they are used to understand higher level concepts. Limits are used to explain certain concepts in calculus. When you take calculus you'll understand. Learning math is a continuous process of learning simple concepts then building upon them to to understand more complicated concepts, and so on. At each step it may not be clear why. My daughter is taking pre-calc and was trying to understand the significance of natural logs (base e). Their real value only comes to light when studying calculus, but you need the basics first. To some degree you need to take it on faith that what you are learning will be useful at some point.
 


I should have probably looked at the other posts but calculus integrates you're previous knowledge of mathematics and gives it precision. Calculus arose mainly as a tool for physics, but also as a refinement of previous mathematics. The biggest difficulty is really understanding the concepts of limits, differentials, and integrals. Beyond that, what you will see is fairly easy i.e. use this theorem, plug in that, follow that rule..blah blah. Calculus really just gives you a number of tools to provide talk about the behavior of functions. It is useful for describing physical phenomena; basically all processes found can be described as differential equations, albeit probably second order nonlinear partial differential equations nonetheless awesome. I'm taking partial differential equations next spring can't wait.
 


To study a limit is to study the *behaviour* of a function as it approaches a certain point.
To provide an example, consider this: Let f(x) = 2x.. What kind of values do we get as we approach x = 5? What happens to the value of f( x ) as x approaches 5?

Let's say we list a couple of these values, values *close* to 5.. let's see what happens:

x1 = 4, f(x1) = 8, x2 = 4.1 f(x2) = 8.2 ... xn = 4.5, f(xn) = 9.. xp = 4.8, f(xp) = 9.6,... xz = 4.9 = f(xz).. f(4.9999) = 9.9998

We can see that as our "input" values go closer and closer to 5, our "output" value goes closer to 10.
If I then continued, f(4.9999999) = 9.99999998... and then finally f(5) = 10! Would it have mattered at all if I said f(5) = 10? You already "knew" that it was approaching 10.. What if I listed the same input/output values but then said f(5) = 1009381304141? Does this make a difference? No, as I said earlier.. we are considering the behaviour of our function AS IT APPROACHES a point, the value (if any) a function takes at the point itself is irrelevant.