Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of WolframAlpha.

WolframAlpha is an answer-engine developed by Wolfram Research that answers factual queries by directly computing the answer from structural data. Note that questions on how to use Mathematica should be asked on Mathematica Stack Exchange.

706 questions
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5 answers

What is imaginary infinity, $i\lim\limits_{x \to \infty} x = i\infty$?

Wolfram Alpha says: $$i\lim_{x \to \infty} x = i\infty$$ I'm having a bit of trouble understanding what $i\infty$ means. In the long run, it seems that whatever gets multiplied by $\infty$ doesn't really matter. $\infty$ sort of takes over, and the…
Archie Gertsman
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40
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7 answers

cubic root of negative numbers

Excuse my lack of knowledge and expertise in math,but to me it would came naturally that the cubic root of $-8$ would be $-2$ since $(-2)^3 = -8$. But when I checked Wolfram Alpha for $\sqrt[3]{-8}$, real it tells me it doesn't exist. I came to…
fasseg
  • 505
31
votes
4 answers

Why does a product $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ lead to infinity?

I asked Wolfram Alpha to compute the following limit: $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ and the answer was $\infty$. I do not understand how this can be, as all elements in the product are smaller than 1. For comparison, when I…
Erel Segal-Halevi
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31
votes
3 answers

WolframAlpha says limit exists when it doesn't?

I was trying to calculate the following limit: $$ \lim_{(x,y)\to (0,0)} \frac{(x^2+y^2)^2}{x^2+y^4} $$ and, feeding it into WolframAlpha, I obtain the following answer, stating the limit is $0$: However, when I try to calculate the limit when $x…
shaqed
  • 475
31
votes
1 answer

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 number $e$, so it's specific to the 11 $e$'s I used…
Dog
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30
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7 answers

How does WolframAlpha get an exact answer here? ${}{}$

I had a simple thing to compute with a calculator: $$\sin\left(2\cos^{-1}\left(\frac{15}{17}\right)\right)$$ I got the decimal answer of about $0.83044983$, but when I typed it in WolframAlpha, it also gave an exact answer of $\frac{240}{289}$. How…
KKZiomek
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29
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4 answers

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?
Templar
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28
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3 answers

Why does Wolfram|Alpha make a mistake here?

We want to evaluate $$\lim_{x \to -8}\frac{\sqrt{1-x}-3}{2+\sqrt[3]{x}}.$$The solving process can be written as follows:\begin{align*}\lim_{x \to -8}\frac{\sqrt{1-x}-3}{2+\sqrt[3]{x}}&=\lim_{x \to…
WuKong
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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? An example of what I want to do: $\binom{n}{k}\cdot p^k \cdot (1-p)^{n-k} = \frac{1}{\sqrt{n\cdot p \cdot (1-p)}}\cdot \frac{1}{\sqrt{2 \cdot…
GunnarBerg
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26
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4 answers

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 of Calculus, obtaining the…
dwarandae
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26
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4 answers

Why does Wolfram Alpha say that $\infty^\infty$ results in "complex infinity"?

When entered into Wolfram Alpha, $\infty^\infty$ results in complex infinity. Why is $\infty^\infty=\tilde\infty$?
esote
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24
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6 answers

Wrong Wolfram|Alpha limit? $ f(x,y) = \frac {xy}{|x|+|y|} $ for $(x,y)\to(0,0)$

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 \gt 0, \exists \delta \gt 0 \diagup \\…
Pablo M
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24
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1 answer

Mathematical Explanation of Mathematica Summation ${\sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)}$

From a mathematical point of view, what phenomena that most likely Mathematica Wolfram encountered when calculating: $$ \sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)\,=\,\color{red}{\frac{2\log(2\pi)-3}{8}+\frac{\zeta(3)}{8\pi^2}} $$ which is…
Hazem Orabi
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Is WolframAlpha wrong? or am I?

Problem : Determine a limit $$\lim_{x\to\infty}xe^{\sin x}$$ exists or not. If it exists, find a limit. Since $-1\le \sin x \le 1$, I can say that $\displaystyle0<\frac{1}{e}\le e^{\sin x}\le e$. Multiply $x$ both side,…
bFur4list
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22
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2 answers

Is this an incorrect proof of $\cot (x)+\tan(x)=\csc(x)\sec(x)$?

If you input the trig identity: $$\cot (x)+\tan(x)=\csc(x)\sec(x)$$ Into WolframAlpha, it gives the following proof: Expand into basic trigonometric parts: $$\frac{\cos(x)}{\sin(x)} + \frac{\sin(x)}{\cos(x)} \stackrel{?}{=}…
Nico A
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