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22

The idea The idea is that if we have $\log(a+b),\qquad a\gg b$ , then we can equivalently write this as $\log a + \log(1 + b/a)$ and the second part will be small, so that one can first compare the first part(s). The power towers with base numbers larger than 1 naturally lead to such logarithms when we repeatedly take the $\log$ of them. So, there ...


16

This now has been discussed in Wolfram blog posts by Michael Trott: Part 1: Making Formulas… for Everything — From Pi to the Pink Panther to Sir Isaac Newton Part 2: Using Formulas... for Everything — From Complex Analysis Class to Political Cartoons to Music Album Covers Here is one of the example apps from blog - go read it in full - fun! Don't miss the ...


12

Artes' guess seems basically right. Here is a way to reach the correct result. First, the antiderivative returned by Mathematica: i0 = FullSimplify[ Integrate[Sqrt[(2 t)^2 + (4 - 3 t^2)^2], t], t > 0] (* (2 (Sqrt[16 - 2 I (-5 I + Sqrt[11]) t^2] Sqrt[8 + I (5 I + Sqrt[11]) t^2] ( 5 (-5 I + Sqrt[11]) EllipticE[ArcSin[1/2 t Root[9 - 5 ...


8

You can set the options for WolframAlpha in the usual way. The option to change is: SetOptions[WolframAlpha, PodStates -> {"Show metric"}] as for me (for whatever reason) it was the default to show metric units, I could verify with: SetOptions[WolframAlpha, PodStates -> {"Show non-metric"}] that this seems indeed to affect also the answers to the ...


5

If you don't want Mathematica to use Wolfram | Alpha for correcting incorrect units, you can just set $AllowInternet = False. The downside of this is that it also blocks internet access for the curated data functions such as WeatherData, FinancialData, etc. You can also use Block to disallow internet only within your function.


5

For indefinite integrals where "Show Steps" is available, the pod state is "IndefiniteIntegral__Step-by-step solution". The following works for cases where W|A can show the steps. showSteps[query_] := WolframAlpha[ "integrate " <> ToString[query], {{"IndefiniteIntegral", 2}, "Content"}, PodStates -> {"IndefiniteIntegral__Step-by-step ...


5

This does not really answer the question as to why Mathematica's Integrate yields an apparently wrong answer. But to simply state why the two answers are different. It seems Wolfram|Alpha does not attempt to do a symbolic integration (which is what your input asks for) before taking its numerical value. As I stated in my comment, using NIntegrate gives the ...


4

I can offer some ideas but it would take work to put together into a package. I'll illustrate with the example sqrt(3)+sqrt(5)pi. val = Sqrt[3] + Sqrt[5]*Pi; Set up an vector of values involving powers of both pi and val. We will work at fairly high precision (300 digits). I chose to go to degree 6 in each, which is overkill for this example but of course ...


4

Here is how you attack this: First click on the little "+" in the right upper corner. Then you select either "Subpod content" or directly "Formula data". Both will result in a more specific request which gives you the hint you need: {WolframAlpha[ "6.38905609893065", {{"PossibleClosedForm", 1}, "FormulaData"}], WolframAlpha[ "6.38905609893065", ...


4

A properly formatted Quantity expression should work just fine, without trying to connect to WolframAlpha servers for conversion. For example, Quantity[1, "Feet"] + Quantity[2, "Inches"] should run with or without internet connectivity. In contrast, Quantity[1, "Foot"] + Quantity[2, "Inches"] will attempt to contact WA servers in an attempt to ...


3

I have no idea why DateListPlot does not work with Quantity. Perhaps it's a bug? But the workaround is very easy: using pattern replacements we extract the numerical values. DateListPlot[nominal /. Quantity[x_, _] :> x, FrameLabel -> {"year", "$ per year"}] Browsing through the help, another option is QuantityMagnitude. ...


3

You can use the RSolve command: RSolve[{a[n] == 1/2 (a[n + 1] + a[n - 1]), a[0] == 1, a[6] == 0}, a[n], n] {{a[n] -> (6 - n)/6}} {{a[n] -> (6 - n)/6}} /. n -> 3 {{a[3] -> 1/2}}


3

I observed this behavior while at a training session at Wolfram Headquarters, and there seems to be an issue with using Integers here: Integrate[Sqrt[(2. t)^2 + (4. - 3. t^2)^2], {t, 0, 2}] // N (* 7.847 *) Specifying Real numbers yields the correct result. I can only assume that Wolfram Alpha is performing this calculation with Real numbers as well.


2

When you say price what do you mean ? Are you talking about retrieving historical market prices for securities i.e shares or are you talking about more complex pricing such as options, futures etc ? You can use the FinancialData[] function to obtain financial data. I would take a subset of your securities and explore FinancialData[] to see what data is ...


2

Well, I'm not sure if you could get historical financial highlights from any place rather than SEC itself... If you want to find historical annual reports per company, please use the following link (remember to substitute "microsoft" with your desired company name): http://www.sec.gov/cgi-bin/srch-edgar?text=microsoft+10-K&first=2003&last=2013 But ...


1

This is not an answer, but comparing the answer with Maple, and also showing step by step integration using Rubi, which might help point to where Mathematica went wrong. Mathematica Integrate r = Simplify@Integrate[Sqrt[(2 t)^2 + (4 - 3 t^2)^2], t] N[r /. t -> 2 - r /. t -> 0, 20] Maple r:=int(sqrt( (2*t)^2+(4-3*t^2)^2),t=0..2); ...


1

To get just the nutrition facts for simpler data use: WolframAlpha["1 whole wheat tortilla + 2 slices american cheese + 150 g steak", {{"NutritionLabelMultiplePlus", 1}, "Content"}] To understand how to get this code use this answer as guide. That other 2nd entry is so complex and long it throws something off in formatting. You can send feedback to ...



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