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 Apr 28 comment exercises for Euclid's Elements You can find some on archive.org. Just search "euclid exercises," or something related. Here's one example: archive.org/details/euclidbookwithn00euclgoog. Also you can just look for copies of the elements and sometimes they put exercises at the end of each book for schools back in the day. hope that helps, I'm looking for some good exercises as well Mar 17 comment Arc length of astroid $x^{-2/3} + 1$ though, right? Jan 7 comment Pouring shampoo into a bottle at 16.5 cm³/s I gave as much info as the book gave me. I don't get the hold. I even included a photo and the questions that I had trouble answering, and the answers! Dec 26 comment Is there an English translation of Diophantus's Arithmetica available? In Steven Hawking's "God Made the Integers" he has books II, III, and V, in English. Dec 17 comment Derive a formula for the volume of the wedge in terms of the constants a, b, c. I'm having trouble connecting it to the 3rd dimension. Another similar triangle? Dec 17 comment Derive a formula for the volume of the wedge in terms of the constants a, b, c. It is the vertical height from the $a$ line, parallel to $c$ Dec 17 comment Derive a formula for the volume of the wedge in terms of the constants a, b, c. Yes I believe so. I see the way I'm doing it now is not working Dec 13 comment What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$? well maybe forget L'Hôpital Dec 13 comment What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$? Could L'Hôpital's rule be applied? It is infinity over infinity. ALso, according to wolfram alpha "lim x->infinity sum (x/(2^sqrt(x)))" returns $51.919191....$ Dec 6 comment The minimum value of $\frac{a(x+a)^2}{\sqrt{x^2-a^2}}$ Oops. It was for an applied optimization problem. It didn't explicitly say "maximum," but I didn't want to include the extra info, just the derivative. I will edit Sep 15 comment $\displaystyle \frac{d}{dx}2^x$ where $x=0$ @Shahar Yes {need more characters} Sep 15 comment $\displaystyle \frac{d}{dx}2^x$ where $x=0$ @user164587 Haha, I hadn't ever noticed that. I'm in Calc 1 and we still use log as base 10 if not specified. And most, if not all calculators, naturally use base 10 Sep 14 comment Prove rigorously: $\displaystyle \lim_{x\rightarrow 2}x^2+5x=14$ So it's like squaring both sides? (But multiplying by equivalents) Sep 13 comment Prove rigorously: $\displaystyle \lim_{x\rightarrow 2}x^2+5x=14$ How did you find $|x-2||x+7|<(9+ \delta)\delta$? Sep 12 comment Prove rigorously: $\displaystyle \lim_{x\rightarrow 2}x^2+5x=14$ $\delta>|x-2|$? Sep 11 comment Derivative at 4, when $f(x)=\frac{1}{\sqrt{2x+1}}$ There was an error in my question (wrong function). This is relevant. Sorry for the confusion Sep 11 comment Derivative at 4, when $f(x)=\frac{1}{\sqrt{2x+1}}$ yes there is an error. will fix in a moment Sep 7 comment Simplifying compound fraction: $\frac{3}{\sqrt{5}/5}$ I know this an old question, but if you had simply changed your √5/5 to a √5/√5, you would've got 3√5÷5/5 and gotten your answer. The whole point of multiplying a complex faction by a number to simplify it is to times it by 1 (√5/√5 in this case) because multiplying anything by 1 is the same thing. Aug 24 comment verify $\lim_{x\rightarrow0}(4x^2+2x+5)=5$ ok I think $|x||4x+2|$ is the answer my professor is looking for Aug 23 comment verify $\lim_{x\rightarrow0}(4x^2+2x+5)=5$ We haven't gotten to delta-epsilon proofs yet