Recent content by lordofpi

So true. I sort of understand why we are taught a certain way; it is of the greatest benefit for greatest number of students who likely will not pursue anything beyond precalculus ever. However, it becomes a horrible impediment to those of us who will or must go on, who would likely have been...

Thanks Michael; I guess that makes sense. The point I couldn't get past, I guess, is that I kept thinking that \forall x \in \mathbb{R}, \sqrt{x^2} = x \neq -x . However, the true definition of the square-root function seems to be that for some number a \in \mathbb{R} we have its square, a^2...

Thanks for the reply Michael. I guess where I am confused is that we are using \frac{1}{x} in the numerator of our multiplier, but then in the denominator we are using \frac{1}{-\sqrt{x^2}}. We ought to be multiplying by the multiplicative identity as we do for other problems of this sort, but...

I think the technique that is to be used for these types of problems, but I just am having trouble grasping why it is permitted. I have no problem with any homework, but it just doesn't seem right. Maybe my text is just not being clear (Larson, 9th, btw) Given a function...

Thanks Dick. Just out of curiosity, what would happen if this were a definite integral? The same, I am assuming, since we would have to subtract -32 from -32?

Homework Statement From Larson, 9th Edition: Section 4.5. Solve the differential equation \frac{\operatorname{d}y}{\operatorname{d}x}=4x+ \frac{4x}{\sqrt{16-x^2}}Homework Equations The Attempt at a Solution Well, I can get my book's answer, but not through doing things in the prescribed way...

I'm sorry if this has already been said, but I'd like to point out that the \sqrt{2} is in fact a real number. Assuming for a minute that we had the tools of perfect accuracy and precision to be able to actually measure the given idealized distances (the difficulty of which has already been...

Thanks chiro for the additional info. And thank you: this place seems to pickup where Usenet left off all those years ago (plus Usenet never had \LaTeX!). I am very excited to be able to participate in the ongoing conversations of so many sharp minds.

Thank you both; that sort of makes sense. I always made use of the slope-intercept form (y=mx+b fairly consistently as well. It just seems to be the most useful of all of the forms. Also, I was very lazy in grade school (decades ago), so -- while I have always had a strong aptitude and love...

I'm in the middle of a calculus course (this is not a calculus question per se), studying from the Larson text, and when an answer to a problem is the equation of a line, I solve for Standard form of a line Ax + By = C. I noticed, however, that the Larson textbook frequently terms answers of...

Great. Thanks so much for putting my mind at ease. It's your statement in your last post that I just wasn't sure of. While it was intuitively correct, math doesn't always work that way, and I didn't want to take any chances of teaching myself some fouled up shortcut :). Funny enough, I just...

Okay, so provided that is all legal, then: If \lvert x-2 \rvert < \delta And \delta = \frac{\epsilon}{3} Then \lvert x-2 \rvert < \frac{\epsilon}{3}\\ \downarrow\\ 3 \cdot \lvert x-2 \rvert < \epsilon\\ \downarrow\\ \lvert 3x - 6\rvert < \epsilon\\ \downarrow\\ \lvert3x - 5 -...

I am familiar with most of how to do ε-δ proofs (even though our professor thought it unimportant to teach it, and our book kind of glosses over it (Larson, Fundamentals of Calculus, 9th), even quadratically, but for some reason I am just getting stuck on what is probably a simple problem...

All great advice, thank you again. Some things will definitely be easier to deal with as a seasoned adult. I'll be sure to post some updates as I wade my way through things. I hope this thread is potentially helpful to others in a similar situation.

All sound advice, thanks. What do you recommend doing in community college specifically? My g/f seems to think I should be taking low-level math courses so that I can take more of them (i.e., if I start with Calc III, Diff. Eq., and Discrete Math, it leaves me very little room to have a lot of...