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Posted by Moby Dick
on 18/9/2009, 3:52 pm, in reply to "Re: Avoiding Division By Zero"
It's helpful to take a look IMO.
x^4 * y^6 - 675 * x^2 * y^3 = 0 simplifies, as we already know, to
x = +/- -5*3^(3/2)/y^(3/2)
Plot this in the range -10 to 10:
plot2d([-5*3^(3/2)/y^(3/2), 5*3^(3/2)/y^(3/2)], [y, -10, 10]);
Now plot it in the range -1 to 1:
plot2d([-5*3^(3/2)/y^(3/2), 5*3^(3/2)/y^(3/2)], [y, -1, 1]);
...and now -0.1 to 0.1:
plot2d([-5*3^(3/2)/y^(3/2), 5*3^(3/2)/y^(3/2)], [y, -0.1, 0.1]);
Now it's clear to me why y cannot be 0. Solving the expression:
x^4 * y^6 - 675 * x^2 * y^3 = 0
for y, and plotting that, turns the graph on its side:
plot2d(3*25^(1/3)/x^(2/3), [x, -10, 10]);
plot2d(3*25^(1/3)/x^(2/3), [x, -1, 1]);
plot2d(3*25^(1/3)/x^(2/3), [x, -0.1, 0.1]);
Obviously, x=0 will result in division by 0 in the expression 3*25^(1/3)/x^(2/3). You can do the algebra, but nether x nor y can be zero when you try to evaluate the resultant expressions.
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