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1d
awarded  Custodian
1d
reviewed Reviewed Exchanging expectation and limits
1d
reviewed Reviewed Markov Chains - Strong Markov Property
1d
comment A negative third derivative implies a positive first derivative at a point.
@Tryss Well I haven't learned about integration yet, so I don't know what the last part tells me :P
1d
comment A negative third derivative implies a positive first derivative at a point.
@MattSamuel I wrote the last derivative using Lagrange's remainder, which is why it's $c$ instead of $x$. Added clarification. Is it wrong?
1d
revised A negative third derivative implies a positive first derivative at a point.
added 47 characters in body
1d
comment A negative third derivative implies a positive first derivative at a point.
@HagenvonEitzen Why must $f'$ average around 0?
1d
asked A negative third derivative implies a positive first derivative at a point.
2d
comment Calculating $\lim_{x\to\infty} (\sin\frac{1}{x}+\cos\frac{1}{x})^x$ without l'Hopital
@anomaly I agree, but I'm preparing for a test, and the instructions say "without l'Hopital's rule"
2d
asked Calculating $\lim_{x\to\infty} (\sin\frac{1}{x}+\cos\frac{1}{x})^x$ without l'Hopital
2d
comment Proving that $\ln ^3|x|=x$ has exactly 3 real solutions
@NikolajK Correct me if I'm wrong, but I am supposed to accept an answer once I understood the solution to my question, am I not? I really wouldn't mind leaving questions open for longer but it does seem like I'm supposed to accept it when I solved it to prevent people putting in effort for nothing instead of answering still open questions.
2d
comment Proving that $\ln ^3|x|=x$ has exactly 3 real solutions
That is exactly what I got to at the end, but thanks for the confirmation :)
2d
accepted Proving that $\ln ^3|x|=x$ has exactly 3 real solutions
Jun
29
comment Proving that $\ln ^3|x|=x$ has exactly 3 real solutions
Actually just the fact that the function must be negative on $(0,1)$ is the obvious thing I was missing ><. Thank you
Jun
29
comment Proving that $\ln ^3|x|=x$ has exactly 3 real solutions
@ClementC. I actually tried that, from the second derivative I found out the minimum and maximum of $f'$ Now I could go to a third derivative as it is already pretty simple, but it's so far I have no idea how to use it in my original problem
Jun
29
asked Proving that $\ln ^3|x|=x$ has exactly 3 real solutions
Jun
17
comment For any closed set $A$ of $\mathbb R$ , does there exists a function $f:\mathbb R \to \mathbb R$ such that, $f$ is discontinuous exactly on $A$?
That what happens when I don't think... Removed
Jun
17
revised For any closed set $A$ of $\mathbb R$ , does there exists a function $f:\mathbb R \to \mathbb R$ such that, $f$ is discontinuous exactly on $A$?
deleted 258 characters in body
Jun
17
answered For any closed set $A$ of $\mathbb R$ , does there exists a function $f:\mathbb R \to \mathbb R$ such that, $f$ is discontinuous exactly on $A$?
Jun
17
comment For any closed set $A$ of $\mathbb R$ , does there exists a function $f:\mathbb R \to \mathbb R$ such that, $f$ is discontinuous exactly on $A$?
What about $f(x)=0$ for $x\in\mathbb{R}\setminus A$ and $f(x)=1$ if $x\in\mathbb{Q}\cap{A}$ and $f(x)=2$ if $x\in\mathbb{I}\cap{A}$. It will be continuous at each point $x_0$ outside of $A$ as it will be $0$ at an environment of $x_0$ (As $\mathbb{R}\setminus A$ is open), and obviously not continuous at $A$.