For questions related to usage of Wolfram Alpha.

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26
votes
1answer
359 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
1k 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 ...
13
votes
4answers
604 views

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

Can anybody explain how this comes about?
13
votes
2answers
382 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: ...
11
votes
2answers
35k 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?
10
votes
1answer
651 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
1answer
712 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
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?
6
votes
4answers
501 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
2answers
154 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
1answer
119 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
1answer
807 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
157 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
1answer
171 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 ...
4
votes
2answers
137 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
741 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
3answers
148 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
892 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
17k 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
1answer
72 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
6k 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
105 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 ...
4
votes
0answers
126 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?
4
votes
0answers
29 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 ...
3
votes
1answer
273 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
107 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
406 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
3k 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
122 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
150 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
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
46 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
544 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
203 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 ...
3
votes
1answer
95 views

What are these numbers?? (floor(a)=0)

I was just so I decided to go and look up the roots of floor(a) 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 ...
2
votes
2answers
761 views

limit of $2^n/3^{n/2}$ as $n\to\infty$

$$ \lim_{n\to\infty}\frac{2^n}{3^{n/2}}$$ 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: ...
2
votes
3answers
665 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
1answer
61 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?
2
votes
2answers
709 views

Comparing integral resolutions using Wolfram Alpha / Mathematica

Equations are in $\LaTeX$ format; I'm still trying to understand how MathJax works. Given the following integral: $\int_0^{+\infty } \frac{1}{x \sqrt{x}} \, dx$ I'm pretty sure that does not ...
2
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} - ...
2
votes
2answers
66 views

Behavior of $f(x) = \sum_{n=1}^x \frac{1}{n}$

I plotted the function $$f(x) = \sum_{n=1}^x \frac{1}{n}$$ in Wolfram Alpha over $x\in\mathbb{R}$ and it gave me some unexpected behavior for negative $x$. This function is obvious for ...
2
votes
3answers
225 views

arithmetic operations on alephs in WolframAlpha

Can someone please enlighten me if or how both of these facts can be true? I entered $\aleph_0-\aleph_0$ into WolframAlpha, which gave the result as undefined. But it also plotted the result on a ...
2
votes
2answers
117 views

WolframAlpha seems to suggest that $log(z) = log(-z)$

Wolfram-Alpha returns this snippet at the end of the "step by step solution": I'm confused by the negation of the expression inside the logarithm. The definition of complex logarithm is: $$log(z) ...
2
votes
1answer
91 views

Is WolframAlpha computing this radical correctly?

Is WolframAlpha computing this radical correctly? $$\sqrt{\frac{1}{1 + {10}^{-375}}}$$ When I double-check again, the inequality: $$\sqrt{\frac{1}{1 + {10}^{-x}}} > 1$$ leads to a ...
2
votes
2answers
166 views

(Wolframalpha) this shouldnt give x=50?

This is my problem: I need x or y for the triangle area that forms between the vertical axis(y) and the function y=100+2x where the area is equal to 2500. so I used for condition to the linear ...
2
votes
1answer
139 views

Can wolfram alpha compute symbolic vector derivatives

Can Wolfram alpha be used to find out say $$\nabla_x\left(\|y-Ax\|_2\right)$$ What command do I use? I tried some obvious ways, and googled a bit, but didn't find anything.
2
votes
2answers
122 views

Solve an equation for a particular variable using Wolfram Alpha

I want to express variable from equation in WolframAlpha web. I tried several keywords but it didn't work. For example I have equation $$y=x+z+k,$$ and I want Wolfram to rewrite it for variable $x$, ...
2
votes
1answer
3k views

How to type logical expressions in WolframAlpha?

Usually WolframAlpha understands what logical expression I have entered but sometimes I can't find a way to do it especially when you are using equivalent sign. For example if I have $$ p \land q ...