Math Is Fun Forum

I guess you are working in Cartesian coordinates?

Then

But I'm not exactly sure what you mean by 'how can I do it in a square?'.

In the meantime, until someone here with expertise on this topic posts, you could also post this on another forum where advanced things are routinely answered:

http://www.chatarea.com/Mathematics

Well at least the basics, I know it is actually a very large language.

(a)

The larger fraction bars act as brackets -- you must carry out the operations on the top first.

Convert to improper fractions.

Multiply the numerators and denominators.

divide 630 and 12 by 6:

It's "\partial" I think .
Here is a test :

Oh, I see.. so it's the derivative of v(t) with respect to the 'variable' p(t), and p(t) itself depends on t.

I guess in the prime notation this would be "v'(t) " where the prime is understood to mean "differentiate with respect to whatever v depends on", in this case p(t) ... I think the prime notation is limited in such cases, since for example say i want to write   d/ds f(t) = 0. The prime notation doesn't have a way to indicate partial derivatives.

As for the physical significance... I guess a(p(t)) means acceleration is dependent on a position function which is dependent on time?

I think a truly fundamental understanding of the chain rule would require writing it out using the limit definition, and then writing the definition of that limit using the delta-epsilon definition of limit.

Which should be equal to:

Now, how to prove that with delta-epsilon is beyond me, I always hated those proofs, but I think that would give a sufficiently deep understanding.

@ cambridge:

as espeon said, just remember to *align the decimal points* for addition and subtraction, make sure that you have them in the same spot in the top and bottom number.
Also remember that you can write as many 0s as you want after the final digit behind the decimal point: for example 1.2 = 1.20 = 1.200 = 1.2000 ...

so say you need to add 1.23 and 2.23432

write it like this for the addition:

2.23432
1.23000
---------

so that the decimals align!

sin and lim , not lin

lim means limit.. for example a number that some sequence is approaching.

What does this approach?
0.9, 0.99, 0.9999, 0.9999999, 0.99999999999, 0.999999999999999999, 0.9999999999999999999 ...

The order of operations of something like this is *innermost operation first*, inside brackets.

So, we first divide, and then take the inverse tangent of the result:

(But remember in which quadrant the point is!)

Is n a real constant? Or a natural number?
Also, how did you get 6x George?

Well I'm not sure, it seems to me that the constants c are arbitrary, meaning that whatever we set them to, we will get an identical curve, but shifted up or down by the amount c.

For example the equation  f = cr - b  defines a "family of lines", and unless you are given some specific points that a specific member of this family must cross, it is not possible to solve for a specific c.

If we knew for example that f must pass through (1, 2) and (3, 4),  then
c - b = 2
4 = 3c - b

and we could solve these to get theconstants. But we don't know any specific points at all here, so I don't think we can solve for specifc constants.
Unless I'm not understanding the question correctly, in which case hopefully someone else can help.

We need a point, call it P, which is on the x-axis, and therefore of the form P = (x, 0)

The distance formula between two points is:

We need the distance between (10, 4) and P to be the same as the distance between (6, 2) and P.

Ie, we need:

to be equal to:

Setting these to be equal:

Square both sides:

Expanding:

Re-arranging:

So the point we need is: