# Tagged Questions

For questions related to usage of Wolfram Alpha.

433 views

### Iterated exponent of $i$

WolframAlpha seems to tell me that $e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^i}}}}}}}}}} = 1$, see link. Is this just an error or is it for real? Adding one more $e$ to the bottom of the tower gives me the ...
2k views

### A limit wrong using Wolfram Alpha

I want to calculate the following limit: $$\displaystyle{\lim_{x \to 0} \cfrac{\displaystyle{\int_1^{x^2+1} \cfrac{e^{-t}}{t} \; dt}}{3x^2}}$$ For that, I use L'Hopital and the Fundamental Theorem ...
72k views

### How to type logarithms in Wolfram|Alpha?

Its sometimes hard to type it if logarithm is not natural and base is not 10, especially if base is variable. So anyone know rules how to type?
2k views

628 views

1k views

### Why is wolfram alpha plotting this differently?

I have an equation for a cylinder as $x^2+(y-b)^2=a^2$ for some $a$ and $b$. so I just plugged in $b=2$ and $a=1$ and tried to plot it using wolfram alpha, and the 3D plot looked like half a cylinder, ...
719 views

### Why WolframAlpha Result is Different?

http://www.wolframalpha.com/input/?i=x%3D10%5E-15%3B+%28e%5Ex-1%29%2Fx When i click Approximate Form in result, the result is: ...
167 views

231 views

### Why doesn't $\lim_{(x,y)\rightarrow(0,0)} xy\sin(\frac{1}{xy})$ exist?

I've tried to get the following limit: $$\lim_{(x,y)\rightarrow(0,0)} xy\sin\left(\frac{1}{xy}\right)$$ wolfram claims it doesn't exist. How to show that? Why can't I take $z=xy$ and receive a ...
158 views

### Why does WolframAlpha give a strange solution set to $\lfloor a\rfloor=0$?

I decided to go and look up the roots of $\lfloor a\rfloor$ in WolframAlpha where $a$ is any number, real or complex, and of course the interval $[0,1)$ showed up as an answer but I also got these ...
631 views

### The sum of digits of $3(3x+3)$ is always $9$ for any $x$ between $1$ and $9$

Given the following 'joke' I stumbled across today It's easy enough to figure out that the answer is always 9. Asshole. However when I tried to 'prove' this for ...
147 views

### Is $2^{\log_2(-5)}$ defined?

As far as I know for $\log_2 x$ to be defined $x$ must be higher than 0. However when I enter $2^{\log_2(-5)}$ into wolframalpha it gives result $-5$. Is it mistake?
1k views

### Is Wolfram Alpha Wrong? (LU Decomposition)

Ok, I've been working on a matrix solver for a while (no, its not going well, thanks for asking), and just discovered something that worrys me alot; The problem at hand is LU Decomposition of a ...
74 views

### Regarding $\lim \limits_{(x,y,z)\to (0,0,0)}\left(\frac{x^2z}{x^2+y^2+16z^2}\right)$--is WolframAlpha incorrect?

$$\lim_{x,y,z\to 0} {zx^2\over x^2+y^2+16z^2}$$ So I am trying to evaluate this limit.. To me, by using the squeeze theorem, it seems that the answer must be zero. I trying using the ...
I wanted to calculate the inverse function of $$f(x) = \frac{1}{x} + \frac{1}{x-1}$$ Quite simple I thought, put $$y = \frac{1}{x} + \frac{1}{x-1} = \frac{2x-1}{x(x-1)}$$ rearrange and solve $$... 5answers 1k views ### Find the second derivative of e^{x^{3}}+7x$$e^{x^{3}}+7x$$Here is what I have tried so far,$$y'=(e^{x^{3}})'+(7x)'y'=3e^{x^{2}}e^x+7y'=3e^{x^{3}+x}+7$$I am supposed to find the second derivative but I believe I have already made ... 1answer 69 views ### Integral of \dfrac{1}{x\sqrt{x^2-1}} I am very confused by this. I know that the derivative of \text{arcsec}(x) is \dfrac{1}{|x|\sqrt{x^2-1}}. However, if you plug in the integral of \dfrac{1}{x\sqrt{x^2-1}} into wolfram alpha it ... 2answers 110 views ### Different results when integrating 1/(x^2-9) with computer tools For checking my calculations, I generally use Wolfram Alpha or a similar tool. Today, I wanted to check the following integral:$$\int {\frac{1}{{9 - {x^2}}}} dx$$From my calculations, using ... 1answer 78 views ### Polar coordinations - problem with r and \theta let's take a look on Archimedean spiral. the polar equation is r = \theta. click here to look. but \tan (\theta) = y/x and r = \sqrt{x^2+y^2}, so r = \theta \rightarrow \tan(\sqrt{x^2+y^2}) =... 1answer 140 views ### Calculating a sum which includes binomial coeffeicients Some formula for calculating the probablity that the difference between the number 6 and the average of accidentally selected 100 points among 10000 points which are distributed in the interval ... 3answers 168 views ### How does WolframAlpha simplify sine and cosine? When I feed WolframAlpha an expression like \sin({\pi\frac{2}{3}}), it correctly prints that this is equal to \frac{\sqrt3}{2}, instead of the decimal expansion 0.866025403\ldots. Perhaps it ... 0answers 1k views ### How can I solve system of linear equations over finite fields in WolframAlpha? Is it possible to solve system of linear equations over finite fields using Wolfram Alpha? If yes, how can I do that? Let us take a system x+y+z=0, 2x+y+2z=0, x+3y+z=0. If I want to solve this ... 2answers 1k views ### limit of 2^n/3^{n/2} as n\to\infty$$ \lim\limits_{n\to\infty}\frac{2^n}{3^{\frac{n}{2}}}$$I used wolfram to get the limit as follows: "lim n tends infinity 2^n/3^(n/2)". And using L'Hospital's rule the result was: \displaystyle\... 1answer 307 views ### How can I construct a 2^63-gon with a straightedge and compass? I entered 2^63 as a stand alone value at WolframAlpha. Among the responses was a factoid that 'A regular 9223372036854775808-gon is constructible with a straightedge and compass.' What is such a ... 3answers 141 views ### Why is \frac{\sum_{n=1}^{\infty} n}{\sum_{n=1}^{\infty} n} indeterminate? We all know that \dfrac{f(x)}{f(x)} = 1 (where f(x) \neq 0) and that \sum_{n=1}^{x} n = \dfrac{x(x+1)}{2}. So, given f(x) \stackrel{\text{def}}{=} \sum_{n=1}^{x} n, we show that \dfrac{f(x)}{... 3answers 445 views ### Wolfram|Alpha returns the wrong result: how can I solve this “high precision” equation?$$1-(1-1.40*10^{-36})^x \ge 1.09*10^{-9}$$I want to estimate x such that the probability on the left becomes larger than the probability on the right. A solution must exist because 1-(1-1.40*10^{... 3answers 4k views ### Using Wolfram Alpha to output table of values over the integers I'm trying to get Wolfram Alpha to output a table of values over the integers for a given function, in example: n^2-n 1----1 4----2 9----3 ... ... (using '-'s instead of ... 2answers 2k views ### Wolfram Alpha: How to show functions with abs() and sgn() as a piecewise function? I was trying to obtain this result: integrate e^|x| dx The result is$$ \int e^{|x|} dx = \frac12 e^{-x} \left( (e^x-1)^2 \operatorname{sgn}(x) -2e^x +e^{2x} - ...
I tried feeding th following integral into WolframAlpha: $$\int_0^2\frac{1}{3\sqrt{x}(\log(x))^{\frac13}},$$ to get an idea of its value. Result: http://bit.ly/strangeint \int_0^2\frac{1}{...