David
Reputation
480
Top tag
Next privilege 500 Rep.
Access review queues
 Mar19 awarded Yearling Feb17 accepted Prove that $f_n$ converges uniformly to $f$. Feb17 comment Prove that $f_n$ converges uniformly to $f$. Ah, so my computation was almost there. I just needed to get rid of the edge case. Feb17 comment Prove that $f_n$ converges uniformly to $f$. @graydad then does that mean there is no way to choose an N, and hence it does not converge uniformly? Feb17 comment Prove that $f_n$ converges uniformly to $f$. Actually, if I assume $e^{1/n} < \epsilon$, then $n < 1/\ln(\epsilon)$, so can I make $N = 1/\ln(\epsilon)$ Feb17 asked Prove that $f_n$ converges uniformly to $f$. Feb17 accepted Prove that for real number $r > 0$ the seq of funcs $f_n(x) = \frac{e^x}{1 + n + x^2}$ converges uniformly on $[−r, r]$ to the 0 function. Feb15 asked Prove that for real number $r > 0$ the seq of funcs $f_n(x) = \frac{e^x}{1 + n + x^2}$ converges uniformly on $[−r, r]$ to the 0 function. Feb15 comment What is the significance of the Uniform Cauchy Criterion vs just being uniformly convergent? I think this question pertains to uniformity of convergence/cauchy criterion, but I think the difference between the two is that with the cauchy criterion, you only need to focus on the values greater than $N$. It eliminates having to think about the rest of the sequence, which simplifies a lot. I think...? Feb15 revised What is the significance of the Uniform Cauchy Criterion vs just being uniformly convergent? deleted 3 characters in body Feb15 asked What is the significance of the Uniform Cauchy Criterion vs just being uniformly convergent? Feb15 comment Inverse proportion - Word Problem I like to think of $k$ as the Constant of Proportionality. So, if we're given a point $B = 5, A = 2$, then they'll give us a Constant of Proportionality, $k$, that relates them somehow. Once we know $k$, we can figure out the respective $B$ or $A$ for any pair. Once you know $k$ relative to a $B, A$ pair you can ask "I wonder what $B$ will be for $A = 10$" or "I wonder what $A$ will be for $B = 15$". Feb15 comment Inverse proportion - Word Problem So, we know that $B^2 * (A + 3) = k$. If we use $B = 5, A = 2$, then we see that $5^2 * (2 + 3) = 125$ because we're substituting in $B$ and $A$. Once we have 125,we know $k$, and $A$ because they tell us that $A = 17$. So, if you go back you see $B^2 * (17 + 3) = 125$ and then you solve for $B$. Essentially, inverse proportion means that as $A$ grows, $B$ shrinks. We know how $B$ and $A$ are related based on $B^2 * (A + 3)$. When someone gives us other values of $B$ and $A$ like $B = 5, A = 2$ we're given an actual point to base calculations off of. Which is how we know $B$ for $A = 17$. Feb15 answered Inverse proportion - Word Problem Feb5 comment What is the radius of convergence of $\sum_{k = 0}^{\infty} 3^{k^2}x^{k^2}$ How does $3^{k^2}$ becomes $(3x)^j$? Feb5 asked What is the radius of convergence of $\sum_{k = 0}^{\infty} 3^{k^2}x^{k^2}$ Feb5 comment Find the interval of convergence for these 3 power series So you're saying you just change $3^{k^2}$ to $3^{k}$ since that would be the $kth$ term? Feb5 comment Find the interval of convergence for these 3 power series In 3 do you do the root test twice? Going from $3^{k^2}$ to $3^k$, and then ultimately $3$? Feb5 comment Find the interval of convergence for these 3 power series I thought you ignore it because its not part of $a^k$ Feb5 comment Find the interval of convergence for these 3 power series Don't you just ignore $x^{2k}$ because it's not part of $a_k$?