RolyPoly
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Questions Asked

RolyPoly:
We have :
\[\int_0^1 \int_{\sqrt{44y^2}}^{\sqrt{44y^2}} \int_{x^2+3y^2}^{4y^2}dzdxdy\]
Task: change the order of integral to dxdzdy
 updated 5 months ago
 44 replies
 2 Medals
Mathematics

RolyPoly:
Integrate f(x,y,z) = z over the region W bounded by z=1, x^2+16y^2 = 16 and z=x+5
 updated 5 months ago
 No Medals Yet
Mathematics

RolyPoly:
\[f(x) =\begin{cases}0 & x = \text{rational}\\1 & x = \text{irrational}\end{cases}\]
Find \[\int_0^1f(x)dx\]
 updated 5 months ago
 40 replies
 1 Medal
Mathematics

RolyPoly:
How to prove that \(\sum_{k=0}^{\frac{n}{2}} C(n,2k) 3^{n2k} = 2^{n1}(2^n+1)\)?
 updated 5 months ago
 7 replies
 2 Medals
Mathematics

RolyPoly:
Suppose in a party of 5 persons, every person brings a gift to the party for exchange. The gifts are distributed back to the persons randoml…
 updated 5 months ago
 No Medals Yet
Mathematics

RolyPoly:
<Double integrals>
How to show that \(\int^1_0 \int_0^2 f(x,y) dy dx\) exists given \(\int_0^2 f(x,y) dy = 2\) ?
 updated 5 months ago
 6 replies
 1 Medal
Mathematics

RolyPoly:
<Double Integrals>
How to get \(\int_0^4 \int_0^{\sqrt{x}} ycos(x^2)dydx\) from \(\int_0^2 \int_{y^2}^4 ycos(x^2)dxdy\)?
 updated 5 months ago
 38 replies
 5 Medals
Mathematics

RolyPoly:
How to find all the critical points of f(x,y) = sinx cosy?
 updated 5 months ago
 5 replies
 1 Medal
Mathematics

RolyPoly:
How to interpret the following question:
Graph the curve \(y^24x^3+4x^4 = 0\) and use the graph to determine where the extrema of f(x, y) =…
 updated 5 months ago
 6 replies
 No Medals Yet
Mathematics

RolyPoly:
Under what conditions on the constant k will the function f(x, y, z) = \(kx^2 + kxz  2yz  y^2 +
\frac{k}{2} z^2\) have a nondegenerate l…
 updated 5 months ago
 3 replies
 No Medals Yet
Mathematics

RolyPoly:
In how many ways can seven identical candies distributed to 3 children {I, II, III} if each child can get any number of candies?
 updated 6 months ago
 30 replies
 No Medals Yet
Mathematics

RolyPoly:
Show that the curve traced parametrically by
\(x(t) = (cos(t  1), t^3  1,\frac{1}{t}  2)\) is tangent to the surface \(x^3 + y^3 + z^3  …
 updated 6 months ago
 21 replies
 2 Medals
Mathematics

RolyPoly:
Show that (p↔q) ⇔ (¬p↔¬q) without using the truth table.
 updated 6 months ago
 9 replies
 1 Medal
Mathematics

RolyPoly:
Can we treat p↔q and ¬(p⊕q) the same thing? They actually share the same truth value, but it just seems a little strange.
 updated 6 months ago
 10 replies
 No Medals Yet
Mathematics

RolyPoly:
\[f(x) =\begin{cases}\frac{xy}{\sqrt{x^2+y^2}} & (x,y)\ne 0 \\0 & (x,y) = 0\end{cases}\]
a) Determine if f is differentiable at (0,0)
b) det…
 updated 6 months ago
 53 replies
 2 Medals
Mathematics

RolyPoly:
In the Computer Science group, it would be better if there was a place for the asker to specify the programming language he/she is using, at…
 updated 3 months ago
 12 replies
 12 Medals
Mathematics

RolyPoly:
If a function f(x,y) is not continuous at the point (a,b), will it be possible that \(\frac{\partial}{\partial x}\)f(x,y) is continous at (a…
 updated 6 months ago
 4 replies
 No Medals Yet
Mathematics

RolyPoly:
How to dual boot Fedora 16 and Windows 8 given that I only have Fedora 16 iso file?
 updated 6 months ago
 6 replies
 No Medals Yet
Mathematics

RolyPoly:
Suppose we unwind adhesive tape from a nonrotating circular tape dispenser so that the unwound tape is held taut and tangent to the dispense…
 updated 7 months ago
 No Medals Yet
Mathematics

RolyPoly:
Suppose we have x apples.
When we distribute them equally to 4 people, 2 apples are left.
When we distribute them equally to 5 people, 3 …
 updated 7 months ago
 3 replies
 No Medals Yet
Mathematics

RolyPoly:
Why is the last two digits of \(91^{71}\) the same as 91mod100? Similarly, why is it true that the last two digits of \(81^{81}\) the same a…
 updated 9 months ago
 82 replies
 1 Medal
Mathematics

RolyPoly:
<Solve the system>
a+c = 1
b+ac+d = 1
…
 updated 9 months ago
 13 replies
 1 Medal
Mathematics

RolyPoly:
<Proof without words>
 updated 9 months ago
 4 replies
 No Medals Yet
Mathematics

RolyPoly:
<Integration>
\[\frac{1}{5}\int \frac{x^3+2x^23x+4}{x^4x^3+x^2x+1}dx\]
 updated 8 months ago
 18 replies
 3 Medals
Mathematics

RolyPoly:
<Integration>
\[\int \frac{2x}{3(x^2x+1)}dx\]
 updated 9 months ago
 3 replies
 1 Medal
Mathematics

RolyPoly:
<Integration>
\[\int (1+y^2)^\frac{5}{2} dy\]
How to start?
 updated 10 months ago
 11 replies
 2 Medals
Mathematics

RolyPoly:
From Mission Impossible to Mission Possible
 updated 10 months ago
 6 replies
 1 Medal
Mathematics

RolyPoly:
<Prob. + Stat.>
Let z be a complex number, show that
\[\sqrt{2}z \ge Re(z) +Im(\bar{z})\]
 updated 11 months ago
 8 replies
 1 Medal
Mathematics

RolyPoly:
<Prob. + Stat.>
a) prove that 1+z+z^2+...+z^n = 1z^(n+1) / (1z) for z \(\ne\) 1
b) Using the result of (a), prove that \(1+cos\theta + co…
 updated 11 months ago
 24 replies
 No Medals Yet
Mathematics

RolyPoly:
<Binomial distribution to Poisson distribution>
How to get \[\frac{\lambda ^k}{k!}e^{\lambda}\] from \[\frac{n!}{(nk)!k!}p^k(1p)^{nk}\]w…
 updated 11 months ago
 13 replies
 2 Medals
Mathematics
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