For questions related to usage of Wolfram Alpha.

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26
votes
1answer
379 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 ...
26
votes
4answers
1k 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 ...
17
votes
4answers
2k views

Wrong Wolfram|Alpha limit?

I have this function: $$ f(x,y) = \frac {xy}{|x|+|y|} $$ And I want to evaluate it's limit when $$ (x,y) \to (0,0)$$ My guess is that it tends to zero. So, by definition, if: $$ \forall \varepsilon ...
15
votes
2answers
45k 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?
13
votes
4answers
632 views

The last few digits of $0^0$ are $\ldots0000000001$ (according to WolframAlpha).

Can anybody explain how this comes about?
13
votes
2answers
395 views

What is the meaning of a number's “representation” on Wolfram Alpha?

When searching a number on Wolfram Alpha, one of the results is its representation. For example, for 8549: 8549 has the representation 8549 = $5·2^6·3^3-91$. Similarly for 75290: ...
10
votes
2answers
198 views

Proof that cos(1) is transcendental?

So, I was playing around on Wolfram|Alpha (as we nerds like to do) and it said cos(1) was transcendental. Could someone provide me with the proof that cos(1) is transcendental?
10
votes
1answer
691 views

How would you input xkcd.com/287 into WolframAlpha?

In this XKCD comic, a stick figure asks an NP-complete problem to order exactly 15.05 worth of appetizers out of a menu that includes the following list of prices: ...
8
votes
1answer
2k views

variable bounds on definite integrals in Wolfram|Alpha

I often have trouble getting Wolfram|Alpha to compute definite integrals with variable bounds, and I'm wondering whether I'm missing something. Some examples: $\int_a^b \sin x\mathrm dx$ and $\int ...
7
votes
3answers
774 views

Integration substitution: How does Wolfram Alpha come up with this step?

I have to integrate $$ \int \frac{1}{(\sin x) (\cos x)} \, dx $$ I looked at the Wolfram Alpha step by step solution to figure out how to do it. First, it rewrites the integral as: $$ \int (\csc ...
7
votes
3answers
2k views

Derivative of floor function

I thought the derivative of function $\text{floor}(x)$ should be $\infty$ for integer values of $x$ and 0 elsewhere. But wolframalpha plot showed something different. Is there any explanation?
7
votes
5answers
103 views

$\sec\theta$ never equals $\tan\theta$. Or does it?!?

Wolfram-alpha is disagreeing with me. I am wondering why: which of us is wrong? I was writing a question to demonstrate why domains of functions matter. The question is: Does there exist an angle ...
7
votes
1answer
878 views

Wrong Wolfram alpha result?

I have this function $$ f(x,y) = \left\{ \begin{array}{ll} \frac{x^3}{x^2 + y^2} & \mbox{if } (x,y) \neq (0,0) \\ 0 & \mbox{if } (x,y) = (0,0) \end{array} \right. $$ And I want to ...
6
votes
4answers
557 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: ...
6
votes
1answer
145 views

Derivative of $\sec^{-1} e^{2x}$, my answer differs from wolfram alpha.

The problem: Find the derivative of $\sec^{-1} e^{2x}$ (\arcsec doesn't seem to work) My work: $u= e^{2x}$ $\mathrm{d}u = 2e^{2x}\,\mathrm{d}x$ The formula I know for the derivative of arcsec(u) ...
6
votes
2answers
177 views

A strange answer for $\int _{-1}^1 \log x\; dx$

I typed $\int _{-1}^1 \log x\; dx$ on Wolfram Alpha. It is giving the answer to be $-2+i\pi$. Can someone please explain what is happening?
6
votes
2answers
78 views

Calculate with sequences from OEIS

Is there any easy way to do calculations with sequences from OEIS online? For example I would like to input something like: (A007620(n+1) / 2 ) + A000027(n) and ...
6
votes
1answer
943 views

How do I plot multi case function in wolfram or geogebra?

How do I plot the following multi case function in wolfram or geogebra? $$ \begin{eqnarray*} f(x) = \begin{cases} 1, &\text{if }x \text{ is an integer}, \\ 0, &\text{if }x \text{ is ...
5
votes
4answers
160 views

Should $x=-2$ be included as an answer for $\frac{x^2+8x+12}{x^2+5x+6}>0$?

$$\frac{x^2+8x+12}{x^2+5x+6}>0$$ First of all while solving inequalities I need to check domain so in this case $$x^2+5x+6\neq0$$ $$x\neq-2,\ x\neq-3$$ Later on ...
5
votes
3answers
108 views

How does Wolfram Alpha come up with the substitution $x = 2\sin u$? Integration/Analysis

I have to integrate $$ \int_0^2 \sqrt{4-x^2} \, dx $$ I looked at the Wolfram Alpha step by step solution, and first thing it does is it substitutes $x = 2\sin(u)\text{ and } \,dx = 2\cos(u)\,du$ ...
5
votes
1answer
185 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 ...
5
votes
1answer
111 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 ...
4
votes
2answers
140 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?
4
votes
1answer
830 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 ...
4
votes
2answers
20k views

Using Wolfram Alpha For Solving A System Of Equations

How do i input the below system of equations in wolfram alpha in order to solve for the unknowns and plot them? If i just say "solve" and input these equations one after the other with a simicolen ...
4
votes
2answers
58 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 ...
4
votes
3answers
201 views

Inverse Function (and WolframAlpha gives different Result)

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 $$ ...
4
votes
5answers
983 views

Find the second derivative of $e^{x^{3}}+7x$

$$e^{x^{3}}+7x$$ Here is what I have tried so far, $$y'=(e^{x^{3}})'+(7x)'$$ $$y'=3e^{x^{2}}e^x+7$$ $$y'=3e^{x^{3}+x}+7$$ I am supposed to find the second derivative but I believe I have already made ...
4
votes
2answers
90 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 ...
4
votes
1answer
77 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}) ...
4
votes
1answer
7k views

Contour integration and wolfram

I am not sure if this is the right site to ask this question, but here it is: Does Wolfram Alpha do contour integrals? If so how might I access that feature. Also, is there an online manual for ...
4
votes
3answers
121 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 ...
3
votes
2answers
912 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: ...
3
votes
1answer
287 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 ...
3
votes
3answers
120 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 ...
3
votes
3answers
424 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 ...
3
votes
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 ...
3
votes
2answers
1k 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} - ...
3
votes
2answers
54 views

Real integral getting numerically evalued to complex number

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 ...
3
votes
2answers
126 views

Wolfram double solution to $\int{x \cdot \sin^2(x) dx}$

I calculated this integral : $$\int{x \cdot \sin^2(x) dx}$$ By parts, knowing that $\int{\sin^2(x) dx} = \frac{1}{2} \cdot x - \frac{1}{4} \cdot \sin(2x) +c$. So I can consider $\sin^2(x)$ a ...
3
votes
1answer
174 views

What's wrong with Wolfram Alpha (or me)? Integral involving exp(-t)

The integral in question $\int e^{-t}\cdot (1+e^{-t})^{-2}dt$ can be solved with an easy $u$-substitution. I'm getting $(1+e^{-t})^{-1}$ which I can verify is correct by derivation. I'm rusty though ...
3
votes
1answer
34 views

Curvature of plane curve, formula disagrees with Mathematica?

I have the following equation $$y=\pi\ln(2x)$$ And when I ask Mathematica/WolframAlpha for the curvature I get $$K=\frac{\pi x}{(x^2+\pi^2)^{3/2}}$$ However the formula for curvature of a plane ...
3
votes
2answers
5k views

Tell Wolfram Alpha that a variable is a natural number

how can I tell Wolfram Alpha that some variables are natural numbers, when I want to solve a equation? Cheers What I want to do: $\binom{n}{k}\cdot p^k \cdot (1-p)^{n-k} = \frac{1}{\sqrt{n\cdot p ...
3
votes
1answer
2k views

Using Wolfram Alpha to solve a system of linear equations

How do I input the below system of equations in Wolfram Alpha in order to solve for the unknowns? I'm wondering if there's some kind of code that can be written in order to make wolfram alpha ...
3
votes
0answers
49 views

Strange things on WolframAlpha: derivation, modulo and doubling result

I asked WA what is the derivative of $\frac1{\cos((x \bmod \pi/2)-\pi/4))}$ equal to for $x=0$. A very strange result came out. The exact result is $-\sqrt2 \mathsf{Mod}^{(1,0)}(0,\frac\pi2)$, ...
3
votes
0answers
726 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 ...
3
votes
0answers
212 views

How to Create a Lesson Plan with Wolfram Alpha

This will be my first post in this forum. I am so excited to see a lot of interesting posting from the community. From the FAQ, I learned that Mathematics stack exchange discussed about mathematical ...
2
votes
3answers
702 views

WolframAlpha blows simple substitution?

I am to find a formula for the n-th derivative of $$\frac{1+x}{1-x}$$ I came up with $$\frac{(-1)^{n+1} \times 2 \times n!}{(1-x)^{n+1}}$$ This seems right, but I noticed that WolframAlpha somehow ...
2
votes
4answers
3k views

Wolframalpha - how to get value of function in a specific point?

For example , given this function - $f(x) = x^3-x^2-x-1$ and I want to check it in the point $x=1.6$. What should I have to write in the command line of wolframalpha in order to get it ?
2
votes
1answer
64 views

The curve $(\cos(\sin x),\sin(\cos x))$ as plotted by Wolfram Alpha

I've just gotten this from Wolfram Alpha: It makes no sense to me. $\cos(\sin x)$ is never zero so how can this curve cross the $y$-axis?