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1d
revised How to factor $X^{20}-1$ in $\mathbb{F}_3[X]$
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1d
revised How to factor $X^{20}-1$ in $\mathbb{F}_3[X]$
added 42 characters in body
1d
answered How to factor $X^{20}-1$ in $\mathbb{F}_3[X]$
2d
answered Can one deduce whether a given quantity is possible as the area of a triangle when supplied with the length of two of its sides?
Aug
26
answered Probability of dying from smallpox?
Aug
26
comment Probability of dying from smallpox?
Andre is pointing out that your third answer is incorrect. You found the complement probability to everyone dying, but you need the complement probability to no one dying.
Aug
26
revised Probability of dying from smallpox?
added 25 characters in body
Aug
26
revised Epsilon Delta definition to prove $\lim_{x\to a} x^{1/3} = a^{1/3}$
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Aug
25
comment Sequence $\frac{(-2)^{n!}}{n^n}$ diverges
Note that since $n!$ is almost always even, the minus sign is just a potential distraction.
Aug
24
revised Solve $x''-(\tan t)x'+2x=0$
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Aug
24
revised Does this function change signs infinitely often?
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Aug
24
revised Is $\frac{4x + 2}{12 x ^2}$ simplifiable?
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Aug
24
answered Is $\frac{4x + 2}{12 x ^2}$ simplifiable?
Aug
22
comment Repeated differentiation of $\frac{1}{1+x^2}$
Sorry, I see now that you see that. Still, why are there no powers appearing? For example, $g^{(2)}(x)=\sum(-1)^n(2n)(2n-1)x^{2n-2}$, and so $g^{(2)}(0)=(2(1))(2(1)-1)=2$, not $1$.
Aug
22
comment Repeated differentiation of $\frac{1}{1+x^2}$
When you are evaluating $g^{(4k)}(0)$, you do should not get $0$ as the result. The first term in the series involves $x^0$, and with $x=0$, that term is nonzero.
Aug
22
comment Repeated differentiation of $\frac{1}{1+x^2}$
$0^0$ needs to be interpreted to be $1$. All other $0^n$ are $0$.
Aug
22
comment $\displaystyle\lim_{n\to\infty}|\sin n|^{\frac{1}{n}}$
An approach: is there a subsequence of $\{n\pi\}$ that approaches $0$ so quickly that $(\{n\pi\})^n\to L<1$?
Aug
22
comment Should I throw the dice again if I have rolled 4?
Almost all of the expert responses here assume a fair die and independence between tosses. In the real world, I don't think either of these would be the case. The degree to which the die is not balanced, and the influence of one roll result on the next may be negligibly small, but it's worth noting that they are there to promote a better understanding of probability modeling versus reality.
Aug
20
comment The number of solutions of $z^5+2z^3-z^2+z=a$ for $a\in \mathbb{R}$
One more note, since it is not explicit here. There is always exactly one real root, since $f'(x)=5x^4+5x^2+(x-1)^2>0$. The lone real root has the same sign as $a$.
Aug
20
comment The number of solutions of $z^5+2z^3-z^2+z=a$ for $a\in \mathbb{R}$
I have added comments to @Micah's answer that (I believe) free it from requiring Wolfram Alpha. Take a look and see if you agree.