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.
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...
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'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?