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8h
comment Linear Operator Boundedness
You forgot to give the definition for the operator.
8h
comment Can someone give me a counterexample to understand why this definition of limit is wrong?
Epsilon could be very, very large..
9h
comment Give an example of three different points in $\mathbb R^3$ such that there are infinitely many planes in $\mathbb R^3$ passing through all of them.
This is exactly what they're asking. In fact if they are noncollinear then there can only be one plane passing through all of them.
17h
comment Relativistic velocity transformation law
That's exactly right!
17h
revised Relativistic velocity transformation law
added 241 characters in body
17h
answered Relativistic velocity transformation law
1d
comment trigonometry - identities and formula, proving
Ahh. Glad you figured it out :) It's an easy mistake to make. I even make these mistakes from time to time.
1d
comment trigonometry - identities and formula, proving
$$\sin(x) - \sin(x)(1-\sin^2(x)) = \sin(x) - \sin(x) - (-\sin^3(x)).$$ Did you forget to properly distribute the negative?
1d
comment Does $\sum 3^{-\sqrt{n}}$ converge or diverge?
@user234494 My logic was that $\frac{1}{3^{\sqrt{n}}}$ should decay very fast since it's a bit like a geometric series. As such, it should decay faster than $\frac{1}{n^2}$ since $\frac{1}{n^2}$ doesn't decay all that fast.
1d
comment Does $\sum 3^{-\sqrt{n}}$ converge or diverge?
A good choice might be $a_n = \frac{1}{n^2}$.
1d
revised trigonometry - identities and formula, proving
added 9 characters in body
1d
answered trigonometry - identities and formula, proving
1d
revised trigonometry - identities and formula, proving
deleted 3 characters in body
1d
comment divergence and curl of the function $(x^2+y^2)\log(1-z)$
@user145608 It probably is a mistake. Even professors and lecturers make them! Sometimes even really embarrassing ones.
1d
comment ring of real functions field or not
No worries! It's an easy mistake to make. I think your second point is a good one worth keeping as an answer since it addresses a very important aspect of function spaces.
1d
comment Solving a system of coupled differential equations
Here's a thought: try taking a second derivative of the first equation to get $2x'''' = -6x'' + 2y''$. Substituting the second equation gives $$2x'''' = - 6x'' + 2(2x-2y+40\sin(3t)) = -6x'' + 4x - 4y + 80\sin(3t).$$ Then noting that $4y = 4x'' + 12x$ from the first equation, you can get an equation for $x$ only. Then try using that to get an equation for $y$ and solve.
1d
comment Solving a system of coupled differential equations
Do not use exclamation points in a title, especially not multiple exclamation points. It's a bit unbecoming.
1d
revised Solving a system of coupled differential equations
edited title
1d
comment divergence and curl of the function $(x^2+y^2)\log(1-z)$
Your function isn't vector valued so it can't have a divergence or curl..
1d
comment ring of real functions field or not
No. Consider $f(x) = x^2$ and $g(x) = x = h(x)$. Then $f(g(x)+h(x)) = f(2x) = 4x^2$ but $f(g(x))+f(h(x)) = x^2 + x^2 = 2x^2$.