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  • 24 votes cast
Feb
7
accepted How can I prove every Riemann sum of x^2 of [a,b] is the integral?
Jan
31
comment How can I prove every Riemann sum of x^2 of [a,b] is the integral?
unless I can show that evenly spaced is equivalent within the same proof, then I wouldn't be satisfied. I have to think about how obvious (to me) it is that they are equivalent, but thank you!
Jan
31
comment How can I prove every Riemann sum of x^2 of [a,b] is the integral?
I was looking for $f(x) = x^2$ rather than $f(x) = x$, although this is slightly different than what I was doing so thank you!
Jan
31
comment How can I prove every Riemann sum of x^2 of [a,b] is the integral?
Ah right I fixed the typo. And yes I see what you mean, you're right of course, they won't cancel. I am moving along to theorems that can be used to prove this, but I'm still curious how one would do it 'from scratch' here.
Jan
31
revised How can I prove every Riemann sum of x^2 of [a,b] is the integral?
typo
Jan
31
asked How can I prove every Riemann sum of x^2 of [a,b] is the integral?
Dec
19
awarded  Caucus
Oct
22
comment The complexity of Depth First Search
The question is about the asymptotic performance of the algorithm. You need to read about 'big O', and the wikipedia article on this subject is a decent place to go. Then, see if you can answer some simpler questions, such as what is the complexity of bubble sort. Finally, tackle DFS!
Oct
22
accepted What is wrong with my limit work here?
Oct
22
accepted Lost in second derivative simplification
Oct
11
comment Prove that all subsequential limits have been found
@Henry yes it appears I was allowed to assume $a_n$ only takes 5 values.
Oct
11
comment Prove that all subsequential limits have been found
@Lund-Nguyen exhaustive was meant to mean '$S$ is the set of all possible subsequential limits' not just a subset, or a wrong set either.
Oct
11
accepted Prove the difference of roots is less than or equal to the root of the difference
Oct
11
asked Prove that all subsequential limits have been found
Sep
28
comment Prove the difference of roots is less than or equal to the root of the difference
I know we can suppose a >= b without loss of generality (since we are using absolute values). However no, I don't see how to move past this part algebraically. I get $-2\sqrt{ab} \leq -2b \to 4ab \leq 4b^2 \to a \leq b$ still not sure what this gets me...
Sep
28
asked Prove the difference of roots is less than or equal to the root of the difference
Sep
10
awarded  Nice Question
Jul
2
awarded  Curious
Apr
22
accepted Markov transition matrix for given problem
Apr
22
revised Markov transition matrix for given problem
added 261 characters in body