Recent content by GFauxPas

If you want to google this, it's called Gabriel's Horn.

One of the definitions of cosine is: ##\cos x = 1 - \frac {x^2}{2!} + \frac {x^4}{4!} - \frac {x^6}{6!}+\ldots## going on forever. If you take only a finite number of terms, then you'll have an approximation. The corresponding series (infinite sum) for sine is: ##\sin x = x - \frac {x^3}{3!}...

The point P = (cosh a, sinh a) on the unit hyperbola gives you an interesting relationship between the signed area bounded by the hyperbola, the horizontal axis, and a line connecting P to the origin. Check out the Wikipedia article on it.

To find the orientation, put t = 0 and t = pi/2 (or put more points if you'd like), and see which way you're going.

They're from the 1980s so they look "old", but "The Mechanical Universe" is a very helpful series of videos on physics. And of course Khan Academy has nice video courses.

I like "Calculus" by Larson and Edwards. I have the 8th edition, but they're up to 10 now. I didn't like how (at least in my edition) they don't go above 3 dimensions, but it's pretty evident how to generalize stuff.

Not sure why this is in the Engineering forum. Mod note: It's now in the Precalc section. One way to prove equality of sets is to show each is a subset of the other. So you want to prove that: ##a \land \neg (b \land c) \implies (a \land \neg b) \lor (a \land \neg c)## ##(a \land \neg b) \lor (a...

I used ##0 \le |\sin x| \le 1##

For someone unfamiliar with Spivak, what are the variables? Numbers?

Unless I'm wrong, it looks like your proof only works for ##\epsilon > 2##. Don't apologize for wasting our time - there's no requirement for us to read your post, after all!

I'd like to see it.

Any time the limit superior of a sequence is not equal to the limit inferior, the limit will not exist.

I'm not sure what you're doing here: but you don't need to do an epsilon delta proof for this one, there's a much much simpler way. What do you know about the limit of a function that's squeezed between two other functions?

Here's my last try, probably.

Maybe try a Weierstrass substitution? ##u = \tan (\frac f 2), \cos f = \frac {1-u^2}{1+u^2},\frac {\mathrm df}{\mathrm du} = \frac {2}{1 + u^2}##