I almost thought that the thread title was cactus.
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Anonymous2008-03-12 15:28
kay so
Most mathematics is about non-changing things like constant velocity, constant acceleration, straight line graphs, Lindsay Lohan's facial expressions etc. Calculus is about things that change like curved lines, variable speed, etc.
Differentiation is all about finding the rate of change of something, (that is finding the slope/gradient of the tangent to a curve.) Integration is the reverse of differentiation and also measures the area between a curve and the x-axis.
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Anonymous2008-03-12 18:37
Calculus:
Yes. Yes, you CAN divide by zero.
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Anonymous2008-03-12 18:46
someone intergrate me the equation of a circle. i have looked all over and i cannot find it. no matter that i do i can't seem to be able to figure it out.
Remember the crucial property of a function y = f(x) is that each x-value produces exactly one y-value.
But for this circle, each x-value produces two different y-values.
For example x = 0 produces the points (0, 2) and (0, - 2).
So the circle x2 + y2 = 4 does not represent y as a function of x.
By a similar argument, a circle will never represent a function y = f(x).
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Anonymous2008-03-13 19:17
A circle equation could be a function depending upon bounds...just thought I'd throw that in.
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Anonymous2008-03-13 20:01
|z| = r
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Anonymous2008-03-13 22:17
POLARS YOU FAGGOTS
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Anonymous2008-03-14 0:34
>>15
If you don't understand what a function is, you don't fucking deserve to know how to integrate.
>>17
The only points at which it does not give two values are the furthest left and right points. And they are just that—two points. A circle is not a function. If that made it a function, then every relation that contained one or more points at which the x-value gave only one y-value could be considered a function.
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Anonymous2008-03-14 0:46
>>12
sqr() is a function. it returns only one value for any given input.
y = x^2 has two solutions. x = sqr(y) and -sqr(y). you have to include the -sqr() err... manually when you solve for x since the square root function only returns a positive number.
Why do we care if a relation is a function anyway; I don't think they bothered to mention important consequences in high school.
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Anonymous2008-03-14 2:53
>>21 since the square root function only returns a positive number.
Maybe in your crappy programming library, but in mathematics, it has two solutions.
bg4 elementary school (or college if you're an americunt)
a)
sqrt(4) = 2
reads like this: which positive number, when multiplied by itself gives us 4? it is 2. (square root of a number is such positive number which when multiplied by itself results in given number)
b)
x^2 = 4 =>
x = 2 or -2
reads like this: which number, when squared gives us 4? it could be -2 or it could be 2.
mathematical writing isn't that cryptic. learn to read it.
"In mathematics, a square root of a number x is a number r such that r^2 = x, or in words, a number r whose square (the result of multiplying the number by itself) is x."
>>32
gb2/algebra1/
If a square root is explicitly stated, it always means the principal—positive—square root. You can only get a ± when you take the root of both sides of an equation when solving for a variable. Wikipedia != authoritative, retard.
positive reals have two square roots, positive and negative, but the square root symbol is usually taken to mean the inverse function of f(x) = x^2. to be a function, it has to produce at most one output for each number, so its commonly the positive one.
i didn't read earlier in the thread to see how it was being used here, but whatever, fuck you guys.
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Anonymous2008-03-15 3:59
it doesn't change the fact that the equation of the circle is not a function. And also, you were arguing that the +/- only comes up when rooting both sides. well guess what, thats exactly what we're doing in isolating y in the circle equation.
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Anonymous2008-03-15 9:37
>>38
I'm not sure who you think you're talking to.
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Anonymous2008-03-15 10:49
>>38
Yeah! Who do you think you're talking too, mister!