Search found 4 matches

by MalachiConstant
Tue Mar 29, 2011 10:35 am UTC
Forum: Mathematics
Topic: What is your favorite proof?
Replies: 41
Views: 5575

Re: What is your favorite proof?

I'm particularly partial to Archimedes' proof for the volume of a sphere. Cantor's diagonalization argument is a close second.
by MalachiConstant
Sun Oct 31, 2010 2:54 pm UTC
Forum: Mathematics
Topic: limit question
Replies: 13
Views: 1594

Re: limit question

Basically, I want to know if it is possible to use the definition of a limit to prove this particular limit without relying on any theorems about limits. So geometry is fine, if we can use it to show for example that |(sin(x)/x)-1|<|x|, rather than using it as a springboard for using the squeeze the...
by MalachiConstant
Sun Oct 31, 2010 11:29 am UTC
Forum: Mathematics
Topic: limit question
Replies: 13
Views: 1594

Re: limit question

My students and I are all aware of the squeeze theorem and the traditional derivation of this limit using the unit circle. My question was to use the epsilon delta definition without relying on some other trick. So we would need to show that |(sin(x)/x)-1|<epsilon whenever |x-0|<delta. Using a graph...
by MalachiConstant
Thu Oct 28, 2010 7:04 pm UTC
Forum: Mathematics
Topic: limit question
Replies: 13
Views: 1594

limit question

Greetings, I'm a long-time lurker and first-time poster. I'm teaching my high school multi-variable calculus class about the epsilon-delta definition of a limit (they didn't learn about it in BC calc because it was removed from the AP a few yeas ago). In doing this, I started wondering if there is a...

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