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Jul
23
comment Fundamental Theorem of Calculus and the left endpoint of the interval.
Well, that makes sense. Thank you
Jul
23
accepted Fundamental Theorem of Calculus and the left endpoint of the interval.
Jul
23
comment Fundamental Theorem of Calculus and the left endpoint of the interval.
He does mention that the value of $b$ can be negative, but that is mentioned as notation for the integral itself, and here in the definitions we have actual intervals where it makes no sense to have $b<a$ (or at least it wasn't defined)
Jul
23
asked Fundamental Theorem of Calculus and the left endpoint of the interval.
Jul
9
accepted A negative third derivative implies a positive first derivative at a point.
Jun
30
awarded  Custodian
Jun
30
reviewed Reviewed Exchanging expectation and limits
Jun
30
reviewed Reviewed Markov Chains - Strong Markov Property
Jun
30
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
Jun
30
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?
Jun
30
revised A negative third derivative implies a positive first derivative at a point.
added 47 characters in body
Jun
30
comment A negative third derivative implies a positive first derivative at a point.
@HagenvonEitzen Why must $f'$ average around 0?
Jun
30
asked A negative third derivative implies a positive first derivative at a point.
Jun
29
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"
Jun
29
asked Calculating $\lim_{x\to\infty} (\sin\frac{1}{x}+\cos\frac{1}{x})^x$ without l'Hopital
Jun
29
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.
Jun
29
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 :)
Jun
29
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