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I'm deeply impressed by mathematics.

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120 Questions

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18	Seems that I just proved $2=4$.
16	Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
13	Show that $\sqrt[3]{2+\frac {10} 9\sqrt 3}+\sqrt[3]{2-\frac {10} 9\sqrt 3}=2$
13	If $f(x)\leq f(f(x))$ for all $x$, is $x\leq f(x)$?
11	Find the minimum of $q$.

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2,976 Reputation

+10	Show that for all $a,b,c>0$, $\frac 1 {\sqrt[3]{(a+b)(b+c)(c+a)}}\geq\frac 3 {2(a+b+c)}$.
+5	Show that $e^{\pi}>\pi^e$.
+70	Show that $d/dx (a^x) = a^x\ln a$.
+10	Solve for $x$, $3\sqrt{x+13} = x+9$

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38 Answers

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10	How to simplify an expression like this: $(x^2+x^{-2}-2)^{1/2}$
7	Show that $d/dx (a^x) = a^x\ln a$.
7	Evaluating tetration to infinite heights (e.g., $2^{2^{2^{2^{.^{.^.}}}}}$)
7	Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$?
6	$\frac{\mathrm d} {\mathrm dx}\sqrt{1/e^x}=$?

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57 Tags

25 algebra-precalculus × 28	7 exponentiation × 2
23 calculus × 25	7 recursion
11 sequences-and-series × 15	6 roots × 4
10 trigonometry × 11	6 polynomials × 4
9 homework × 15	3 integral × 7

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