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Dec
17
comment Question involving entire functions
Dear pankaj, you have now asked three questions, all of which show no own work. Try investing a little time in the material before you come to us, and if you had any thoughts, please tell us what you've tried.
Dec
17
comment boundedness of an operator
$\frac{f(x)}{1+|x|+|y|}\leq f(x)$
Dec
17
comment Show a function is continuous
Okay, so $\lim_{x\to1}F(x,x-1)-(x-1)\sin(1/x)$ should be defined by continuity of F and convergence of the term $(x-1)\sin(1/x)$ (convergence because $x-1\to0$ and $\sin$ is bounded). But this limit is your $x\sin(\frac{1}{x-1})$, which indeed does not converge since $\frac{1}{x-1}$ does not (add a few sentences here), ergo $F$ is not continuous.
Dec
17
comment Show a function is continuous
I don't know, your reasoning sounds alright but you'll need to add a sentence somewhere - I'm not quite convinced.
Dec
17
comment Show a function is continuous
The fact that your calculations do not work does not prove $F$ cannot be continuously defined. In particular, the fact that the individual limits do not exist does not prove that the sum does not (for example, consider $0=\lim 1/x - 1/x=\lim1/x-\lim1/x$).
Dec
17
comment Displaying $2 \cdot 10^5$ as $200000$
Right click on the result, Numeric formatting.
Dec
17
comment Prove that $\int_0^{+\infty} \frac{\ln x}{a^2+x^2} dx = \frac{\pi\ln a}{2a}$
Perhaps this is not an answer for Leitingok, but this is exactly how they would do it in the book, and shows the power of complex analysis. +1.
Dec
17
comment Given joint pdf of $X$ & $Y$, find pdf $Z=XY$
Yes. $X\leq1$ and $Y\leq1$ so $Z=XY\leq1$.
Dec
16
comment $f^{-1}$ and continuity
This is actually one of the definitions for continuity, so you really need to explain what definition you are using.
Dec
16
comment linear hyperbolic PDE with some BCs at infinity
Hello there, try putting your equations in latex, as explained here: meta.math.stackexchange.com/questions/107/…
Dec
16
comment Prove that $f'$ exists for all $x$ in $R$
You make quite a stronger statement than what was asked for, but it's technically correct.
Dec
16
comment Complex Functions Concept Questions
I think the fact that these answers are longer than the normal, mathematical, equation-rich answers, says enough about this method of teaching.
Dec
16
comment Prove that $f'$ exists for all $x$ in $R$
Related: math.stackexchange.com/questions/151032/…
Dec
16
comment Prove that $f'$ exists for all $x$ in $R$
Related: math.stackexchange.com/questions/175607/…
Dec
16
comment Prove that $f'$ exists for all $x$ in $R$
Possible duplicate: math.stackexchange.com/questions/64766/…
Dec
16
comment How to find $f'$ from the definition of derivative?
... so what is $f'(0)$?
Dec
15
comment How random is the digits of $\pi$?
If any of you guys have more requests, I'll be happy to compute/plot more data.
Dec
15
comment How random is the digits of $\pi$?
@PeterSheldrick: mathematica: Histogram[RealDigits[Pi, 10, 10000][[1]], 10]
Dec
15
comment Find the coordinate matrix of the function $\cos^2x$ relative to the ordered basis $\{1,\cos x,\sin x,\sin 2x\}$.
Since when are sets ordered?
Dec
12
comment In a fraction between integers, what denominators produce a periodic result?
Every ratio has periodic decimals, if that's what you're asking.