Functions – What is the minimum value of this nested radical?

Similarly, what is the maximum value of this nested radical? I want to share a similar nested radical, but this time with varying breaking forces.

What is the minimum value of $$ f_ infty = frac {x} { sqrt {x- sqrt[3]{x- sqrt[4]{x- cdots}}}} $$ Where do the radicals rise by one each time?

  • Here is a plot of $ f_ {19} $, We can see that as $ x to 1 ^ + $, $ min f_ {19} to $ 1,7186 which is strange because the denominator can only accept the binary values $ 0 $ or $ 1 $ at the $ x = 1 $, The curve increases from monotonous $ 1 $ continue what is expected as the counter dominates.

Enter the image description here

  • Actually a simulation in PARI / GP up $ f_ {100} $ gives a minimum value of around $ 1,718,565That's a bit close $ e-1 $although I strongly doubt it will ever reach that value.

  • Note that $ f_k $ is defined in $ (1, infty) $ for all positive integers $ k $but the curve is swinging wildly $ (- infty, 1) $,

Another interesting question: Why is the minimum value of $ f_k $ for big $ k $ not equal to the expected $ 0.1 $ or $ pm infty $? Can you manipulate? $ f_ infty $ so L & # 39; hopital can be used to determine the value of $ 1,718 cdots $?

Functions – apply color to the larger value between two table cells

I have a table with player names and their score.

Player A | 58 | 45 | Player B
and so on
I want player A | highlight 58 in green color as the value is larger than player B.
Accept player on cell A1I have passed
to go conditional formatting then New rules
Use a formula to specify the cells to format
$ A <> $ B and choose green as color.
But it does not change to OK.

(I could not enter EXCEl in TAGS coz's request of 200 reputation)

Plot – ParametricPlot table with complex functions in multiple charts

Suppose I have a table with complex functions like

M = 10;
G = table[Sin[i p] + p I, {i, M}]

I want to parameterize them in graphs. Each graphic contains only one of them. What do I have to edit in the following code?

ParametricPlot[Evaluate[ReIm /@ G]{p, 0, 2},
AxesLabel -> (Style[#, 12, Bold] & / @ {Re, Im}),
PlotRange -> {{-1.2, 1.2}, {0, 2}}, ImageSize -> 600,
PlotLegends -> Placed[G, Right]]

Which they represent in the following single graphic:

Enter the image description here

Thank you in advance.

Summation – What is the probability that two samples for some aggregate functions will have the same results?

Imagine, I have a list of $ N $ Floating-point numbers with normal distribution, and I take a sample of $ n $ Calculate elements without replacement, summation, mean, and sample variance, replace $ n $ Elements, take another sample of $ n $ Elements without replacement, and calculate the summation, mean and variance of the second sample.

If the summations, means, and variances between the two samples are the same, what is the probability that the two samples will consist of the same numbers?

dnd 5e – Can Cleric functions be applied to my spell cast for clerics / wizards with multiple classes and vice versa?

Unless a class / domain feature says otherwise, they work. In fact, the rules for multiclassing are mentioned especially for the Channel Divinity feature. The important part of it is:

… Whenever you use this feature, you can choose one of the Channel Divinity effects from both classes.

Specifically, this refers to sourcing the Channel Divinity feature from multiple sources, but it also means that the effects can affect qualifying spells / attacks from both classes.

Machine Learning – Neural network does not train due to functions that are not loaded

I'm trying to train a neural network on Mathematica 11.3.
However, NetTrain does not work and outputs the following error:

"The function" WL_MXGetVersion "was not loaded from the file

(See attached picture).
What can I do against it?

Enter the image description here

rust – Calling functions in the implementation of a feature function

Consider the following example: I have a property foo with a function foo () and an associated type Fand a structure bar what is implemented foo,

barImplementation of foo () is so complicated that I would like to call a smaller function func () to structure the code. As I understand it, I can not add functions impl foo for bar block because func () is not part of foo Feature. So you have to be on your own impl bar Block. Here is what I finally invented:

Feature Foo {
Type F;
fn foo (& self) -> Self :: F;

Structure bar {}

impl foo for bar {
Type F = i32;
fn foo (& self) -> Self :: F {
(even as a & bar) .func (3)

impl bar {
fn func (& self, f: :: F) -> :: F {
f + 1

fn main () {
Let b = bar {};
println! ("{}", ());

But is that the idiomatic way to solve my problem? Slightly less important if I need more helper functions func ()Is there a way to shorten :: F? (Insert a kind Declaration at the top level of the impl bar block certainly does not work as it would in a range of functions.) I would have want to?