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[Zrk2]

Electric field is a vector field. It's components are projections to some directions and can be negative without problems.

The way you arrived to 280x-560y it seems that you treat S as X+Y. That is likely wrong. Electric field as vector is E=(280x, -560y) and you should take the length of the vector (280*3, -560*2) to get the answer you are probably looking for.

That's right, thanks. What I had to do was calculate the x and y components and hten use Pythagorean theorem to put them back together. That makes the next part of the question much easier too.

[Skyrunner]

" The function f(x) is defined as f(x) = ^{(sqrt(x2 + 9) - 3)}/_x², where x ≠ 0. 
If f(x)  is continuous in the interval (–∞, ∞), what is the value of f(0)?"

The answer is 1/6, but how can f(0) exist when x ≠ 0? :<
The answer of 1/6 was obtained by using limits...

[Jim Groovester]

If that is a direct quotation of the problem then the problem is extremely poorly posed. Is the quote accurate?

f(x) is indeed undefined at x = 0, and f(x) is not continuous on the interval (–∞, ∞), but regardless of the mathematical inaccuracy of the problem, what they want you to do is to use L'Hopital's rule to find the value of the limit of f(x) as x -> 0.

Really, though, you should protest such a poorly posed problem by boldly declaring on your paper that f(x) is undefined at x = 0 and stick to your guns.

[Skyrunner]

As I thought. O_o
It's in Korean, but it should be accurate.
I forgot to mention that x ∈ R, excluding 0.

[Karlito]

So, the problem deliberately goes out of its way to point out that x=0 isn't in the domain right before asking you to evaluate x=0? Sheesh.

[MagmaMcFry]

"The function f(x) is defined as f(x) = ^{(sqrt(x2 + 9) - 3)}/_x², where x ≠ 0. If f(x)  is continuous in the interval (–∞, ∞), what is the value of f(0)?"

Terminology mixup? Here's the same question with proper words:
"A real function f satisfies f(x) = ^{(sqrt(x2 + 9) - 3)}/_x² for all real x ≠ 0. If f is continuous, what is the value of f(0)?"

[Pnx]

Relatively simple math question for precalc.

I've got 10x³-4x²+15x-6=0

It says the answer is:

Spoiler (click to show/hide)

2/5

But I seem to be having trouble getting to that answer.

[MagmaMcFry]

Well, it's pretty easy (at least for me) to see that 10x³-4x²+15x-6 = (2x²+3)(5x-2), and since the left factor has no real zeroes and the right factor has the zero 2/5 the answer must be 2/5.

[Pnx]

I knew it was going to be something that would leave me kicking myself, all this time I'd been trying to get it into a quadratic form... Thanks.

[Skyrunner]

I have figured out a rough estimate of God's minimum power in watts, based on the size of the Revelation city and the mention that God has enough glory to brighten the city up like day, and a few simplifications (mainly that the city just happens to be a perfectly flat plane ).

Problem is, I don't know how to find the volume of a f(x,y) formula >_> Neither does Wolfram Alpha, apparently.

Code: [Select]

4767400000000000*e^(-0.01 * sqrt(x^2 +y ^2 + 1))or

So... any guides to how to find the volume? xD The equation approaches 0 in all directions.

[ed boy]

Problem is, I don't know how to find the volume of a f(x,y) formula >_> Neither does Wolfram Alpha, apparently.

Code: [Select]

4767400000000000*e^(-0.01 * sqrt(x^2 +y ^2 + 1))or

So... any guides to how to find the volume? xD The equation approaches 0 in all directions.

Are you integrating from -infinity to +infinity in both the x and y directions?

Although the function does tend to 0 in all directions, that isn't always enough by itself, though in this case, it tends to zero in a way that does make it integrable.

A handy shortcut in maths is that pretty much whenever you see x^2 + y^2, you can change into polar co-ordinates. This means that, with the change of variable, we want to solve:


which can be integrated, and equates to 19999Kπ

[Skyrunner]

May I ask what K is? Is it the big number I had in front of Euler's number?

[ed boy]

May I ask what K is? Is it the big number I had in front of Euler's number?

Yep.

[Skyrunner]

Interesting. So God emits at least 299 exawatts of power.

[MaximumZero]

Well, now I know that I have to hit 300. Thanks.