Recent content by gb7nash

That sounds right. So you rewrote your problem as 2 \int_{3}^6 f(x)dx - \int_{3}^6 3 dx? The first part is fine, but the bolded part doesn't make any sense. If you're working with a definite integral...

Well, technically it still is, just not on f(x). You still have to integrate 3.

If this is your problem word for word, then you need to get confirmation on what the problem is. Like Mark said, the conclusion to this "problem" is false. I'm guessing the problem is to find \int_{3}^6 (2f(x) - 3)dx, but nobody here will know unless you find out what the true problem...

Correct.

How did you get this? In any case, what makes this problem more complex is the 1/x2 exponent, so it's not as simple as just applying l'hopitals rule. I would take the natural log in the beginning, find the limit, and apply exponentiation.

This is fine so far. Try evaluating e1r. What two pieces of information can you conclude? Similarly...

Does the problem specifically say there are only two distinct answers? If so, it is still possible to get just two distinct roots (they'll just be repeated roots). Assuming you did everything right up to this point, I would suggest trying the rational root theorem. If that fails, you could...

Correct. Cosine is bounded between -1 and +1. You don't want to use integers. That's what the epsilon is for. By letting ε > 0, this covers every case.

No. I'm asking why you're setting ε = |x(3-cos(x^2)|. Yes. -1 ≤ cos(x2) ≤ 1, so: |x(3-cos(x2)| ≥ |x(3-1)| = |2x| > |x|. This is the opposite of what you want.

For future reference, use | for absolute value. It's easier to read. Is the problem to show that \lim_{x \to 0} f(x) = 0? I'm not sure where this comes from. The bolded part is good start. I'm not sure why you're equating epsilon to |x(3-cos(x2)|. Neither of these statements are true...

You can. All of your steps are valid. Why do you think you can't do this? (as a side note, you could simply just divide both sides by i)

I'm not an expert at all on theoretical physics and what math it uses, but as far as the math essentials go, you'll want to know: differential equations several variable calculus proofs linear algebra abstract algebra real analysis As far as anything beyond that, there are a lot of branches of...

Correct.

The two bolded things are what you want to prove. Once you have those, then the conclusion follows. Before you do anything, what is a in your problem? What is b? Once you have a and b, what is the first thing you need to prove?

Let's look at the definition of the square root: If a2 = b and a ≥ 0, then a = √b. Now look at your problem. What two things do we have to prove?