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29m
revised Find the limit for both
added latex
2h
revised Seeking proof for the formula relating Pi with its convergents
added latex
3h
comment Solve exponential equation $3^x= 2^x+2$
@FlybyNight It was just a guess, but good to know.
3h
comment Solve exponential equation $3^x= 2^x+2$
The short answer to your question is no. There may be a way to represent the solution in terms of the Lambert-W function, but I wouldn't exactly call that an elementary method.
3h
comment Trigonometric manipulation
en.wikipedia.org/wiki/…
Jul
6
comment Integral of factorial function
This makes me curious if we can at least find a value for the definite integral from $0$ to $1$, which would give us an explicit equation for your linear approximation.
Jul
6
answered Guess explicit formula using iteration
Jul
5
comment Evaluation of $\int_0^1 \frac{\log(1+x)}{1+x}\log\left(\log\left(\frac{1}{x}\right)\right) \ dx$
Got it. As an historical aside, I'm somewhat curious as to the etymology behind labeling the digamma function by the capital Greek letter 'psi' as opposed to, oh I dunno, the Greek letter 'digamma'? :) Also, thanks in particular for the reference.
Jul
5
comment Evaluation of $\int_0^1 \frac{\log(1+x)}{1+x}\log\left(\log\left(\frac{1}{x}\right)\right) \ dx$
Could you kindly point me towards a definition of the function $\Psi(n)$? I'm drawing a blank.
Jul
5
comment Integration Help Needed to Calculate Arc Length of a Vector-Valued Function
No, sorry. If the problem your professor gave to you is correctly stated, then I have I no idea what he/she intended.
Jul
5
comment Integration Help Needed to Calculate Arc Length of a Vector-Valued Function
That's because the integral is unsolvable. It doesn't matter how much time you have to work the problem. It's a typo.
Jul
5
comment Integration Help Needed to Calculate Arc Length of a Vector-Valued Function
Where did you encounter this integral? Is this for a research paper?
Jul
5
comment Integration Help Needed to Calculate Arc Length of a Vector-Valued Function
Are you sure the second component shouldn't be $4(\color{red}{\cos t} + t\sin t)$ instead?
Jul
5
comment Integrate $\tan^4(\theta)$
@Ian I completely agree this way is much harder. That's part of the reason I suggested trying to solve it this way.
Jul
5
answered Integrate $\tan^4(\theta)$
Jul
5
comment On a certain series of complex numbers
@Alex.Unger First of all, the integer powers of $i$ cycle through four possible values, not just two. See cirpis's response for details. Second of all, the only thing that matters when deciding if a series is geometric or not is if all pairs of consecutive terms have a common ratio. In this case the common ratio is $i$.
Jul
5
answered On a certain series of complex numbers
Jul
5
comment On a certain series of complex numbers
Also, en.wikipedia.org/wiki/Finite_geometric_series#Related_formulas
Jul
5
answered On the number of digits for irrational numerical base systems
Jul
5
comment How to show that $\lim\limits_{n\to\infty}n^{2/3}a_{n}=\sqrt[3]{2}/\Gamma{(1/3})$
@PranavArora Heh, I didn't figure it out at all. WolframAlpha told me that it's so, therefore it must be so. Is that obvious enough for you? =D