nbouscal
 Name:
 Nathan Bouscal
 School:
 The Internet
 About:
 Knowledge is power; ignorance is bliss.
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Questions Asked

nbouscal:
Group Title
If x is a nilpotent element of a commutative ring R, prove that 1+x is a unit in R.
 updated 2 years ago
 5 replies
 2 Medals
Mathematics

nbouscal:
Group Title
Prove that if \(R\) is an integral domain and \(x^2=1\) for some \(x\in R\) then \(x=\pm1\).
 updated 2 years ago
 3 replies
 1 Medal
Mathematics

nbouscal:
Group Title
Show that if A is a basis for a topology on X, then the topology generated by A equals the intersection of all topologies on X that contain …
 updated 2 years ago
 1 reply
 No Medals Yet
Mathematics

nbouscal:
Group Title
Prove that a linear transformation is norm preserving if and only if it is inner product preserving.
 updated 2 years ago
 6 replies
 2 Medals
Mathematics

nbouscal:
Group Title
Prove that \(\int_a^bf\cdot g\le(\int_a^bf^2)^\frac12\cdot(\int_a^bg^2)^\frac12\).
 updated 2 years ago
 3 replies
 1 Medal
Mathematics

nbouscal:
Group Title
Proof of the triangle inequality on Euclidean nspace.
 updated 2 years ago
 12 replies
 1 Medal
Mathematics

nbouscal:
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Diagonalize the matrix: \begin{bmatrix}1&i\\i&1\end{bmatrix}
 updated 2 years ago
 12 replies
 1 Medal
Mathematics

nbouscal:
Group Title
Determine the Jordan form of the matrix \(\begin{bmatrix}1&1&0\\0&1&0\\0&1&1\end{bmatrix}\)
 updated 2 years ago
 4 replies
 No Medals Yet
Mathematics

nbouscal:
Group Title
Okay, let's try a different question. Still linear operators.
(a) Let A=\(\left[\begin{matrix}a & b\\c&d\end{matrix}\right]\) be a real mat…
 updated 2 years ago
 46 replies
 3 Medals
Mathematics

nbouscal:
Group Title
Let A and B be 2x2 matrices. Determine the matrix of the operator T: M>AMB on the space \(F^{2x2}\) of 2x2 matrices, with respect to the ba…
 updated 2 years ago
 27 replies
 No Medals Yet
Mathematics

nbouscal:
Group Title
Analysis study @Limitless @inkyvoyd
 updated 2 years ago
 1 reply
 No Medals Yet
Mathematics

nbouscal:
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Here's a fun question.
Is there a set \(K\) in \(\mathbb R^2\) that intersects every line exactly twice?
…
 updated 2 years ago
 3 replies
 No Medals Yet
Mathematics

nbouscal:
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I know we have talked a lot about the medal system and its strengths and weaknesses. I have two ideas that I think would help strengthen the…
 updated 2 years ago
 7 replies
 3 Medals
Mathematics

nbouscal:
Group Title
I think it might be beneficial to have some representation of grade or study level available, preferably in the hoverover user info window.…
 updated 2 years ago
 5 replies
 1 Medal
Mathematics

nbouscal:
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Prove that if a metric space is sequentially compact, it is also compact.
 updated 2 years ago
 9 replies
 No Medals Yet
Mathematics

nbouscal:
Group Title
A walkthrough of the integration of \(\sqrt{\tan x}\).
 updated 2 years ago
 8 replies
 5 Medals
Mathematics

nbouscal:
Group Title
Partial fraction decomposition: \(\dfrac{2x^2+7x1}{x^3+x^2x1}\) I've factored the denominator into \((x^21)(x+1)\), and set up my system…
 updated 2 years ago
 4 replies
 1 Medal
Mathematics

nbouscal:
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Integral question (see inside)
 updated 2 years ago
 27 replies
 2 Medals
Mathematics

nbouscal:
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Integration question (inside)
 updated 2 years ago
 19 replies
 3 Medals
Mathematics

nbouscal:
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I would really appreciate it if there was a way to disable the blinking chat window, or even to leave chat entirely while still remaining in…
 updated 2 years ago
 22 replies
 3 Medals
Mathematics

nbouscal:
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Logarithmic differentiation (see inside)
 updated 2 years ago
 2 replies
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Mathematics

nbouscal:
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Can someone doublecheck this derivative for me? In comments, may take a minute to typeset.
 updated 2 years ago
 9 replies
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Mathematics

nbouscal:
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 updated 2 years ago
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Mathematics

nbouscal:
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Another derivative (see inside)
 updated 2 years ago
 12 replies
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Mathematics

nbouscal:
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Particle A moves along the positive horizontal axis, and particle B along the graph of \(f(x)=\sqrt{3}x,x\le 0\). At a certain time, A is a…
 updated 2 years ago
 36 replies
 2 Medals
Mathematics

nbouscal:
Group Title
Proof of the derivative of \(f(x)= \sqrt{x}\) (see inside)
 updated 2 years ago
 7 replies
 2 Medals
Mathematics

nbouscal:
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Another epsilondelta problem.
(In answers so I can use equation editor)
 updated 2 years ago
 6 replies
 3 Medals
Mathematics

nbouscal:
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Determine the limit l for the given a, and prove that it is the limit by showing how to find a d such that f(x)l<e for all x satisfying 0…
 updated 2 years ago
 14 replies
 2 Medals
Mathematics