Thread Killer - Gaming Edition (PG13)

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Where's your mama gone, where's your mama gone?
Where's the baby gone, where's your mama gone?

far far away!

where's your papa gone, where's your papa gone?
Where's the baby done, where's your papa gone?

far far away!
far far away!

Last night I heard my mama singing this song
boooooogie, tschppitschppi tschi tschi
walked out this morning and my mama was gone
boooooogie, tschppitschppi tschi tschi tschppitschppi tschi tschi tsch

Where's your mama gone? Where's your mama gone?
Where's the baby done, little baby gun?
Where's your mama gone? Where's your mama gone?

far far away!

Where's your papa gone? Where's your papa gone?
Where's the baby done, little baby gun?
Where's your papa gone? Where's your papa gone?

far far away!
far far away!

Last night I heard my mama singing this song
boooooogie, tschppitschppi tschi tschi
walked out this morning and my mama was gone
boooooogie, tschppitschppi tschi tschi tschppitschppi tschi tschi tsch

Let's go now!

Last night I heard my mama singing this song
boooooogie, tschppitschppi tschi tschi
walked out this morning and my mama was gone
boooooogie, tschppitschppi tschi tschi tschppitschppi tschi tschi tsch

All together now!

Last night I heard my mama singing this song
boooooogie, tschppitschppi tschi tschi
walked out this morning and my mama was gone
boooooogie, tschppitschppi tschi tschi tschppitschppi tschi tschi tsch

One more time now!

Last night I heard my mama singing this song
boooooogie, tschppitschppi tschi tschi
walked out this morning and my mama was gone
boooooogie, tschppitschppi tschi tschi tschppitschppi tschi tschi tsch

I wanna hear you singing now!

Last night I heard my mama singing this song
boooooogie, tschppitschppi tschi tschi
walked out this morning and my mama was gone
boooooogie, tschppitschppi tschi tschi tschppitschppi tschi tschi tsch
 
Dixie said:
What is this crap with short posts!? :mad:
Click to expand...


This brings back fond memories:

Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a function and a point in the domain, the derivative at that point is a way of encoding the small-scale behavior of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called the derivative function or just the derivative of the original function. In mathematical jargon, the derivative is a linear operator which inputs a function and outputs a second function. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling function is given the input three, then it outputs six, and if the squaring function is given the input three, then it outputs nine. The derivative, however, can take the squaring function as an input. This means that the derivative takes all the information of the squaring function—such as that two is sent to four, three is sent to nine, four is sent to sixteen, and so on—and uses this information to produce another function. (The function it produces turns out to be the doubling function.)

The most common symbol for a derivative is an apostrophe-like mark called prime. Thus, the derivative of the function of f is f′, pronounced "f prime." For instance, if f(x) = x2 is the squaring function, then f′(x) = 2x is the doubling function.

If the input of the function represents time, then the derivative represents change with respect to time. For example, if f is a function that takes a time as input and gives the position of a ball at that time as output, then the derivative of f is how the position is changing in time, that is, it is the velocity of the ball.

If a function is linear (that is, if the graph of the function is a straight line), then the function can be written y = mx + c, where:....etc,etc.

Enjoyed Das Calculus.

/Fetches the bucket and mop and follows Dixie.
 
m=[d]y/[d]x....

This gives an exact value for the slope of a straight line. If the graph of the function is not a straight line, however, then the change in y divided by the change in x varies. Derivatives give an exact meaning to the notion of change in output with respect to change in input. To be concrete, let f be a function, and fix a point a in the domain of f. (a, f(a)) is a point on the graph of the function. If h is a number close to zero, then a + h is a number close to a. Therefore (a + h, f(a + h)) is close to (a, f(a)). The slope between these two points is

m=f(a+h)-f(a)/(a+h)-a

which is f(a+h)-f(a)/h....
 
Cool, eh?

:D

...This expression is called a difference quotient. A line through two points on a curve is called a secant line, so m is the slope of the secant line between (a, f(a)) and (a + h, f(a + h)). The secant line is only an approximation to the behavior of the function at the point a because it does not account for what happens between a and a + h. It is not possible to discover the behavior at a by setting h to zero because this would require dividing by zero, which is impossible. The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero:

lim h->0 f(a+h)-f(a)/h

Geometrically, the derivative is the slope of the tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients. For this reason, the derivative is sometimes called the slope of the function f.

Maths only really started to interest me once we started Calculus....unfortunately.
 
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