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| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 1 year, 8 months |
| seen | May 19 at 3:02 | |
| stats | profile views | 143 |
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May 19 |
revised |
How to solve this integral easily: $\int \frac{x\cdot \sqrt[3]{x+2}}{x+\sqrt[3]{x+2}} dx$ added dx to the integrand |
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May 19 |
comment |
Why is $\varphi$ called “the most irrational number”? http://www.ams.org/samplings/feature-column/fcarc-irrational1 |
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May 19 |
suggested | suggested edit on How to solve this integral easily: $\int \frac{x\cdot \sqrt[3]{x+2}}{x+\sqrt[3]{x+2}} dx$ |
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May 9 |
awarded | Notable Question |
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Mar 23 |
comment |
$\sqrt{\frac{a}{2}}+\sqrt{\frac{a}{2}}\ge \sqrt{a}$? Or you could just end with $\sqrt{2}\sqrt{a}=\sqrt{2a} > \sqrt{a}$ instead of having to explain that $\sqrt{2}>1$. |
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Mar 23 |
comment |
$\sqrt{\frac{a}{2}}+\sqrt{\frac{a}{2}}\ge \sqrt{a}$? This is good informal reasoning but not a good proof. If you start out by assuming a conjecture is true and then arrive at a tautology, that does not necessarily prove that the conjecture is true. It just shows that the consequence of it being true is a tautology. |
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Mar 23 |
suggested | suggested edit on $\sqrt{\frac{a}{2}}+\sqrt{\frac{a}{2}}\ge \sqrt{a}$? |
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Mar 6 |
comment |
How to understand why $x^0 = 1$, where $x$ is any real number? The idea that exponentiation can be represented as iterated (repeated) multiplication really only holds for natural number exponents. Think about negative exponents: what is 5 times itself, negative 2 times? It doesn't make sense in our minds, even though we know the value of $5^{-2}$. Even worse is with rational, and worse, irrational, exponents. Mathematically we have a way of calculating them, but we don't tend to think of them as iterated multiplication. This concept breaks down when we get to 0-valued exponents as well. |
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Mar 4 |
revised |
name this function added 146 characters in body |
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Mar 4 |
revised |
name this function added 146 characters in body |
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Mar 4 |
comment |
name this function I like your ideas but they're all piecewise. Is there one not piecewise? Is there one that has infinitely many derivatives (continuous everywhere or perhaps even uniformly continuous)? |
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Mar 4 |
revised |
name this function added 146 characters in body |
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Feb 11 |
revised |
Fibonacci numbers that are powers? edited body |
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Feb 11 |
comment |
name this function I've tried these, they do not fit all the criteria. Neither the logistic function nor the erf function meet both $f(1)=.5$ and $f'(0)=1$. (the erf function is the integral of the Gaussian curve you mentioned in your post) |
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Feb 11 |
comment |
name this function because $\frac{d}{dx} \left(\frac{2}{\pi} \arctan(x)\right) \ne 1$ at $x=0$ |
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Feb 11 |
comment |
name this function Interesting: $f'$ is bounded by $1$, $f''$ is bounded by $2$, $f'''$ is bounded by $6$, $f^{\mathrm{iv}}$ is bounded by $24$. Is $f^{\mathrm{n}}$ always bounded by $n!$? |
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Feb 11 |
asked | name this function |
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Feb 10 |
asked | Fibonacci numbers that are powers? |
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Feb 10 |
revised |
which is the cardinal of primes? simplified hyperlink, changed Aleph to Aleph-naught |
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Feb 10 |
comment |
which is the cardinal of primes? Just because there is no formula for a bijection does not mean there isn't a bijection. The common misunderstanding that a lot of people have is that functions need to have "formulas" or "equations". This is not always the case. Check out the Dirichlet Function. |
