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Dec
8
comment Graph Theory triangle (3 colors)
I don't understand. If you properly edge-color $K_n$ with $n$ colors, no intersecting edges can have the same color, so any triangle must have distinct colors?
Dec
8
comment A good source for linear algebra on matrices
So you need something for abstract algebra with examples from linear algebra, or linear agebra theory, like vector spaces?
Dec
8
comment How can I rotate a point 45 degrees counterclockwise around any point?
@Nichols you are likely better off with $x' = x \cos \theta - y \sin \theta$
Dec
8
comment Finding Transformation inverse
@lllll this is only true about linear transformations from $\mathbb{R}^m$ to $\mathbb{R}^n$, you are transforming a function space.
Dec
8
comment optimization with non smooth constraint
@JesseRJ MATLAB is not a good solver. Maybe CVXOPT? abel.ee.ucla.edu/cvxopt/examples/index.html There are others that are free. The best paid one is CPLEX sold by IBM
Dec
8
comment optimization with non smooth constraint
@JesseRJ Modern optimizers have a special type for that constraint.
Dec
8
comment optimization with non smooth constraint
@JesseRJ are you using linear optimization only, or can you have binary variables?
Dec
8
comment optimization with non smooth constraint
@JesseRJ I don't understand your comment, likely a part got deleted by accident?
Dec
8
comment Find $\lim_{x \to -8} \frac{\sqrt{1 - x} - 3 }{ 2 + \sqrt[3] {x}}$
@omidh Please see the update, can you finish it now? Feel free to accept the solution when you understand it to the end...
Dec
5
comment expected value - two etaps
Likely, etaps means stages and eagle means tail.
Dec
5
comment Find $\lim_{x \to -8} \frac{\sqrt{1 - x} - 3 }{ 2 + \sqrt[3] {x}}$
Do you know derivatives? can you use L'Hospital's rule?
Dec
5
comment Find $\lim_{x \to -8} \frac{\sqrt{1 - x} - 3 }{ 2 + \sqrt[3] {x}}$
PLease exhibit your work on the problem and we will be glad to give some hints. How about expanding the root in the numerator into Taylor series around $x=1$?
Dec
5
comment What am I doing wrong? (using the formula for lowering powers)
@Cherry_Developer Because $\cos(4x)$ is one object, and also $-\cos(4x) \neq cos(-4x)$
Dec
4
comment What am I doing wrong? (using the formula for lowering powers)
@Cherry_Developer Exactly
Dec
4
comment Laplace transform involving two functions of t
Also, if you are integrating in $dr$, $f(t),g(t)$ go outside of the integral. If you are integrating in $dt$ , you need to set $r = -s$, not $r=s$ as you suggest
Dec
4
comment Laplace transform involving two functions of t
Depends what you want, wikipedia lists a pretty nasty identity for what you tried to do (en.wikipedia.org/wiki/Laplace_transform)
Dec
4
comment Laplace transform involving two functions of t
What are $f$ and $g$? What is the integral with respect to, $dt$ or $dr$???
Dec
2
comment In a limit proof, what are the assumptions?
@Amad27 Generally, to prove such things, you fix some arbitrary $\epsilon > 0$ and find the value of $\delta_2$, such that for any $x \in (a-\delta_2,a+\delta_2)$ you will have the desired inequality $||f(x)|-|L|| < \epsilon$.
Dec
2
comment Calculation of all positive integer $x$ for which $\displaystyle \lfloor \log_{2}(x) \rfloor = \lfloor \log_{3}(x) \rfloor \;,$
you likely want $\ln x$ in the last inequality?
Dec
2
comment Innovation behind formula for surface area and volume of a sphere
@Half-Bloodprince here is the original Euclid's proof of that fact: aleph0.clarku.edu/~djoyce/java/elements/bookXII/propXII10.html