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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
Dec
2
comment Innovation behind formula for surface area and volume of a sphere
@Half-Bloodprince You should be able to find easily the geometric proof that the cone is 1/3 the volume of the circumscribing cylinder.
Dec
2
comment Innovation behind formula for surface area and volume of a sphere
@Half-Bloodprince Also a standardized summation of simple shapes argument. Here is an example of derivation using a method of disks (which I don't like): mathforum.org/library/drmath/view/55263.html
Aug
31
comment 2 examples to try to understand partials derivatives and deriviability
A discontinuous function is not differentiable. In any number of dimensions. You can design a continuous variant that would be differentiable, but that would not be the function itself.
Aug
28
comment Omega Notation and Average Running Time Problem
@MounaMokhiab think about how you compute average-case running time for an algorithm. you compute what it's performance is on a set of all possible inputs and take the average. when you take the average, it may do bad on a very small section of inputs but do ok on the rest - since you are averaging over a very large quantity - it will take out any factor of your choice. Randomization was just a simplest way to give an example of this.
Aug
28
comment There is no nonconstant entire function $f$ such that $f(z+1)=f(z)$ and $f(z+i)=f(z)$
Makes sense to me
Aug
28
comment Omega Notation and Average Running Time Problem
@MounaMokhiab yes, same method as Snufsan described in the above comment: toss $f(n)$ coins if all heads, waste $n^n$ time and do something in $n^2$, else do something in $n^2$. Total running time is $2^{-f(n)} n^n + (1-2^{-f(n)}) n^2$ and now if $f(n)$ is large enough you are good to go.
Aug
28
comment Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?
Yes, they are different, but where both are defined (i.e. on the intersection of domains) - the values will coincide.