Recent content by mrg

I'm a big fan of Lang's textbooks, and his book on Calculus I and II is great. It's rigorous in that it contains proofs and he explains where things come from, but it isn't over the top (the infamous epsilon-delta proofs are saved for an appendix, for example). The other really great thing about...

Good afternoon, I've been working my way through Serge Lang's series of textbooks, and I recently completed A First Course in Calculus. I'm currently working through the sequel to that book, Multivariable Calculus, and that should keep me tied up for at least two months. Looking ahead...

Agreed completely, td21. It's a wonderful, elegant, and beautiful way to approach mathematics that has been mostly lost, I'm afraid. Although many contemporary math books contain formal definitions and proofs, the emphasis is squarely placed on the skills and procedures by which to calculate...

I actually didn't use it; I thought about some of the drawbacks and decided it wasn't in my students' best interests. As you've said, it is a bit antiquated in some respects. But my biggest gripe was that it was missing some skills that students need (the complete lack of any coordinate plane...

Got it. Thanks for the help!

It's a limit of the form $$\lim_{x\rightarrow a} \frac{f(x)}{g(x)}$$.

Homework Statement $$\lim_{x\rightarrow -2^-}\frac{x}{x^2+x-2}$$ 2. The attempt at a solution Clearly, when graphing the above equation, the limit does not exist (or approaches positive infinity). However, when applying L'Hopital's Rule, we have $$\frac{1}{2x+1}$$ and then we can go ahead and...

I knew it was something stupid. No idea where I got x from. Thanks Sammy.

Homework Statement $$ \int x^{3}cos(x^{2})dx$$ The attempt at a solution OK, so I am aware that there is a way in which to do this problem where you do a substitution (let $$u=x^{2}$$ to do a substitution before you integrate by parts), and I was able to get the answer right using this method...

Homework Statement I'd like to see a proof that lim x->0 x/sinx = 1. Homework Equations It is given that lim x->0 sinx/x = 1 The Attempt at a Solution [/B] I can confirm this limit quite easily by graphing - the curve obviously approaches one, and the left- and right-handed limits are...

1. Simplify the algebraic expression you get for Δy and Δy/Δx for the equation y=2^x 2. Use the difference quotient (f(x+h)-f(x))/h. No use of chain rule or other shortcuts. 3. I've tried a host of things, including raising terms to a natural log power (I.e. e^(ln2)*x*h), using...

I just touched on this very concept with my high school geometry class. In order to derive the formula for the area of a circle, we assumed that a circle was an "infinity-gon." Then, using the formula A=(1/2)ap (where a is the apothem and p is the perimeter) we substituted in the radius for a...

You're correct Eigenperson. I want to share with my honors students one of the most read and studied works of art of all time. Plus, there is a great deal to learn from the structure of it, the amount of proofs, etc. As you say though, there are some initial concerns with how the modern-day...

AlephZero, micromass, and homeomorphic: Thank you for your excellent replies. I greatly appreciate the guidance and wisdom you've given me. I'll be looking into the books that were suggested, and giving them serious consideration. I'd love to hear from others, as well. What are your opinions...

Thanks for the reply Tobias. The link you've provided contained some very useful information and I thank you for sharing it. While I agree with you that I will need to go through the material for most all high school students for them to truly get it, Euclid's book is vastly different from...