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 Jun 1 comment Differentials in the argument of a function This reminds me of what you do when you write out a semi-discrete finite difference method. $$\partial _t\text{f(t,x)=}\partial _x\text{f(t,x)}$$ $$f(t+\Delta t,x)(2\Delta x)=f(x+\Delta x)-f(x-\Delta x)$$ May 21 comment Is there a typo in Calculus:Early Transcedentals? Actually I'd say it's a fairly common mistake. It's a side effect of calculatoritis and the calculus books not really discussing error in more than a cursory way. May 18 comment sum of an infinite series It's interesting to note that original series is absolutely convergent, but $\sum a_n$ and $\sum b_n$ are conditionally convergent. By the Riemann rearrangement theorem, they can be resummed to any real, but the LHS is of course invariant. So what's the deeper justification? May 18 comment Function in inner product I deleted my comment since it just inelegantly repeated what came above. :P May 18 comment Function in inner product What about if we define $F(u)=proj_{(v^\perp)}u=k{v^\perp}$ for some $k\in R$. Then $\left=0$ but $F(u)$ is not zero unless $v =0$. Or am I being daft? May 17 comment How to graph $x\sin(x)$ I think it's useful to think of functions like $f(x)\sin(x)$ where $f(x)$ acts like an envelope or a varying amplitude, and draw $f(x)$ as Anrdé recommends. For the periodic part, $g(x)=x\sin(x)$ must satisfy $g(x+T)=g(x)$. It's easy to see this is not the case for any $T\neq0$. May 16 comment Difference in limits because of greatest-integer function Or in the same spirit: $$\lim_{x \to 0} \lfloor 1-x \rfloor$$