# Patrick Reardon

 Feb 24 awarded Yearling Feb 24 awarded Yearling Jun 8 awarded Caucus May 8 comment Integrate $\int{2^{2x}} dx$If you just divide your answer by $\ln(2)$ then you'll get Wolfram's answer. And you're right, $2$ and $e$ are both constants and they almost share the same properties, at least relative to integration of the corresponding exponentials. $e^x$ is a bit cleaner though since dividing by $\ln(e)$ amounts to dividing by $1$.. Apr 26 comment Prove that if $A$ is null and $f: \mathbb{R} \longrightarrow \mathbb{R}$ has a continuous derivative, then $f(A)$ is nullDo you know about absolutely continuous functions? They preserve null sets, and any function with a continuous derivative is absolutely continuous. Apr 26 comment Let $a_{n}$ be a sequence such that $(a_{n})^{2}=ca_{n-1}$ where ($c>0,a_{1}>0$).Prove that $a_n$ converges to $c$.@Peter: Not a big deal, but it wasn't true as stated, that's all. I thought mathematicians were supposed to be picky :) Apr 26 comment Let $a_{n}$ be a sequence such that $(a_{n})^{2}=ca_{n-1}$ where ($c>0,a_{1}>0$).Prove that $a_n$ converges to $c$.Right, but in your first line you claim that convergence implies that the limit is $c$. In this case that is the limit, but the correct statement in the first line would be that it certainly converges to either $c$ or $0$. Apr 26 comment Let $a_{n}$ be a sequence such that $(a_{n})^{2}=ca_{n-1}$ where ($c>0,a_{1}>0$).Prove that $a_n$ converges to $c$.The statement about convergence of the nth root of $a$ is only valid for $a>0$. That condition holds here but isn't what you stated. Apr 26 comment Let $a_{n}$ be a sequence such that $(a_{n})^{2}=ca_{n-1}$ where ($c>0,a_{1}>0$).Prove that $a_n$ converges to $c$.From the second displayed line, the limit could be $0$ as well, whereas $c>0$. That it's not requires at least some argument. Apr 24 revised Predicate Logic Argument Validityadded 413 characters in body Apr 24 revised Predicate Logic Argument Validityedited body Apr 24 revised Predicate Logic Argument Validityedited body Apr 24 answered Predicate Logic Argument Validity Apr 17 revised Inner product in $\mathbb{R}^2$ and angles of a triangleeditted TEX formatting Apr 17 revised Inner product in $\mathbb{R}^2$ and angles of a triangleTEX edit: < to \langle and > to \rangle Apr 17 revised Inner product in $\mathbb{R}^2$ and angles of a triangleTEX format Apr 11 comment Continuity by ContradictionThe negation you want is: $(\exists \varepsilon >0)(\forall \delta_n=\frac1{n})(\exists x_n)$ so that $|x_n-0|<\delta_n$ and $|\sqrt{x_n}-0|>\varepsilon$. You're missing the $\exists x_n$ part. Apr 11 comment Showing a function is negativeThe domain of $f$ doesn't include $0$ because of the $\log(p)$ terms. How did you get $f(0)=0$? Apr 10 awarded Scholar Apr 10 accepted What's the probability that three points determine an acute triangle?