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Flowreckoning is a kind of scorelore. anent how things shift.
Anis a worth that shifts through scores. For , x is a widespread unknownworthing. This worth, x, can be any score. However, if we have another unknownworthing, such as y, we can link the unknownworthings with a . For byspel, this is a worthlink:
$ y = x $
This worthlink says that for each worth of y, x is the same worth. If we have a y worth of 2, the x worth is 2 also. Here is another worthlink:
$ y = 2x $
This worthlink says that for each worth of y, x is two times that worth. If we have a y worth of 2, the x worth is 4, since 2 * 2 = 4.
Worthdrawings and WorthspeedEdit
Once we have a worthlink, we can draw a seenlyof that worthlink, handling each worth of one unknownworthing with the worth of the other unknownworthing.
On a worthdrawing, two $ y = x $:at a right stand for the worths of x and y. As the unknownworthing y shifts from one score to the next, a is marked at the worth of x, getting these worths from the worthlink. For byspel, here is the worthdrawing for the worthlink
The worthdrawing makes a straight thread since each worth of the unknownworthing y is the same as the unknownworthing x. This means that the worthdrawing is shifting from one score to the next at an $ y = x $ is 1, since the unknownworthing x is shifting at the same speed as the unknownworthing y.speed. The is the speed at which one unknownworthing's worth is shifting with heed to the other. The worthspeed of the worthlink
Straightforwardly, the worthspeed is the shift in the unknownworthing y over the shift in the unknownworthing x. We can then work with the following worthlink when finding worthspeed: Δy / Δx.
See the worthdrawing $ y = 1/2x $:
The worthspeed of this worthdrawing is again Δy / Δx, so the worthspeed is $ 1/2 $.
In the byspels above, the worthspeed has been unshifting. However, let us see the worthdrawing of a worthlink with a $ y = x^2 $:,
Here, the worthspeed is shifting, it is not like the above, where the worthspeed is always 1, or always 2. We can find theof this worthdrawing, or how fast its worthspeed is shifting.
The worthspeed at anyon the worthdrawing is the worthspeed of a , a thread that hits the worthdrawing at only one nib. To find the worthspeed of this grazing thread, we will again use our worthlink, Δy / Δx. However, this worthlink needs two nibs of x and y in order to be handy; this worthlink would give us the worthspeed of a , a threat that hits the worthdrawing at two nibs. Thus, how could we find the worthspeed at just one nib?
As the Δx between two nibs becomes smaller and smaller, the worthspeed of the crossing thread becomes more and more naught, 0, for the worthspeed of the grazing thread to be reckoned. We must then take the as Δx naught.to the worthspeed of a grazing thread. This means the Δx must be
In this bound, however, Δx will be h. We will be finding the bound as h atsteps naught of the crossing line, to find the worthspeed of the grazing thread. We will abide by the same worthlink to find worthspeed: Δy / h. If $ y = x^2 $ is our worthspeed, the shift in y would be $ (x+h)^2 - x^2 $. Putting this together, the bound is:
After working the bound, we would find that this bound actually evens to $ y = 2x $. This means that at any nib on the worthlink $ y = x^2 $, the worthspeed is $ y = 2x $. This second worthlink that tells us the worthspeed of any nib on a first worthlink is called the speedshift.