Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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42 views

On multivariable functions and graphs

The definition of graph from Wikipedia is the following: In mathematics, the graph of a function f is, formally, the set of all ordered pairs $(x, f(x))$, and, in practice, the graphical ...
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0answers
33 views

How does one test whether a positive integer is semiperfect in Wolfram Alpha?

Wolfram Alpha allows to test whether a positive integer $n$ is abundant, deficient or perfect. However, I was not able to find a way to test whether $n$ is semiperfect (i.e., equal to the sum of all ...
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1answer
34 views

How to plot all points that are defined by $(4\kappa+2(\lambda \mod 2), 2\lambda\sqrt 3)$ in Wolfram Alpha?

How to plot all points that are defined by $(4\kappa+2(\lambda\mod2), \ 2\lambda\sqrt 3)$ for some $\kappa$ and $\lambda$ that are integers in Wolfram Alpha? I just want to know what this set of ...
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1answer
106 views

What is this strange notation in the output of Wolfram Alpha?

For some reason I need to find the values of two positive integers $k$ and $x$ such that: $$ k x^3 (2 x + 1)^3>2 (k + 1) (x + 1)^2 (2 x^4 + 2 x^3 + 3 x^2 + 2 x + 1). $$ Inputting this in Wolfram ...
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1answer
56 views

What is meant by `DiracDelta'[t]`?

While calculating an inverse Laplace transform Wolfram Alpha returned to me the following output: ...
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3answers
57 views

How to calculate this sum with binomials?

In this paper An Improved Algorithm for Decentralized Extrema-Finding in Circular Configurations of Processes from 1979, in chapter with analyze of average number of passes messages I found this ...
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1answer
60 views

What is happening here? [Wolfram]

When I input: $2^{a/b} = (2^a)^{1/b}$ Into Wolfram Alpha, it produces a very strange looking "implicit plot": I'm entirely sure what this means or what it's even trying to plot and how. I suspect ...
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1answer
332 views

Wolfram Alpha: Simple Arithmetic with named constants replacement

I want to verify an equation I implemented in a computer programming language using WA. For example: $\frac{s^2}{((s+w_0)(s+w_1))}$ And specify values for $s, w_0,$ and $w_1$. I have tried: $\...
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0answers
54 views

How to use Wolfram to draw Cantor function?

I want to have a close look on the image of $\frac{1}{2x} + \frac{1}{2}$ Cantor function, which is a rigidly increasing one. I look up in the Wolfram and it told me it has a symbol called ...
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0answers
127 views

Wolfram Alpha and Fourier Transform inconsistencies?

I've been using Wolfram Alpha for the Fourier Transform because our professor doesn't require us to use the actual definition to solve for the Fourier Transform. Rather, he doesn't mind if we use ...
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0answers
37 views

How to find volume of two curves about an axis

Question- $R$ is the region bounded by $y=\sqrt{x}$ and $y=\frac{x}{2}$ and this region is rotated around $x=4$. What is the volume? My attempt $$\left|\pi\int_0^2 ((4-2y)^2-(4-y^2)^2) \right| \, ...
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7answers
7k views

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 ...
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2answers
152 views

Is there a way to set the precision of the answer given by Wolfram Alpha/Mathematica?

I did this: Expand[(6.54928x+0.22365x^2)(2306.685568-1.79917x^3-39.98117494x^2+47.818846x)] and got this: 15107.1 x + 829.069 x^2 - 251.153 x^3 - 20.7251 x^4 - 0.402384 x^5 However, I want all ...
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1answer
248 views

Is there a way to solve a very complicated equation in one variable? [closed]

Essentially solving for x in this equation: $\frac{(631.60353-0.078408πx^3-3.44416x^2)[π(\sin31.72778)+2]}{6.54928x+0.22365x^2} + 15.4-\frac{x(\sin31.72778+2)+7.7}{6.54928x+0.22365x^2}(0.235224πx^2+6....
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1answer
35 views

Why does conversion from base $b_1$ to $b_2$ give this strange result in Wolfram Alpha?

I was trying to convert the $5$-ary number $44444444_5$ to base $25$ using Wolfram Alpha: 44444444 from base 5 to base 25 Curiously, I got the result $0000_{25}$....
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72 views

Why is the solution to this sum of two sines so complex?

While working on a signal processing problem, I found I needed to solve a certain equation involving a sum of a sequence of sines. Since I wasn't really sure how to do this cleanly, I decided to ask ...
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2answers
46 views

Limit of a function that I think is undefined

The $\displaystyle\lim_{x\to \infty}\ln(x)\sin\left(\frac{1}{x}\right)$, wolfram computes it to be $1$. However the limit of $\ln(x)$ is infinity and $\sin(1/x)$ is $0$, the product of these are ...
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1answer
78 views

Why does the integral for this function not exist

I'm trying to integrate this function on Wolfram Alpha, but it says "no result found in terms of standard mathematical functions". $$\frac{\alpha t^{\alpha-1}e^{-(t/\beta)^\alpha}}{\beta^\alpha}$$ ...
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3answers
266 views

Fourier transform of $t^2$ discrepancy

I encountered a discrepancy when taking the fourier transform of $t^2$ that I don't understand. I would expect $\mathcal{F}[t^2]$, $$\mathcal{F}[t^2]=\int_{-\infty}^\infty t^2 e^{-i \omega t}dt$$ to ...
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0answers
110 views

How can I plot y vs x with multiple terms/variables? [closed]

I am trying to plot a ($y$ vs $x$ style) graph with Wolfram Alpha, but the syntax needed is a little more involved. I started with: ...
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1answer
48 views

What does s(n) = s(n) mean?

I'm trying to create python analogue of wolframalpha's PartitionsQ function which calculates number of distinct partitions of integer. I found documentation about this function http://mathworld....
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5answers
128 views

Calculate domain $f(x)=x^{\frac{x+1}{x+2}}$

I have the following function: $$f(x)=x^{\frac{x+1}{x+2}}$$ I tried to calculate the domain, which seems easy, and my result is: $D(f)=(0,\infty)$. When I tried to calculate it, by using Wolfram-...
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3answers
92 views

Calculate $\lim_{x \rightarrow 0^+} \frac{\arctan (\log (1+\sqrt x)) \sin^3(x^{3/4})}{(e^{\tan(x)}-1)(1-\sin^2(x))}$

I'm trying to calculate the following limit: $$\lim_{x \rightarrow 0^+} \frac{\displaystyle\arctan (\log (1+\sqrt x)) \sin^3(x^\frac34)}{\displaystyle (e^{\tan(x)}-1)(1-\sin^2(x))}$$ For ...
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2answers
123 views

Why wolfram alpha assumed $ x>0$ as a domain of definition for $x^x $?

I'm confused why wolfram alpha defined the function $x^x $ for $x>0$ , only what i think that it were defined it as :$e^{x\log x}$ , but the domain of definition depend to the function form .then : ...
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1answer
144 views

How can I input a function $f$ and then evaluate an expression like $f(a) - f(b)$ in WolframAlpha?

Is there a WolframAlpha command that would allow me to input a function and then evaluate an expression containing it? For instance I have a lengthy function like $f(x) = \frac{x^3 + \sin(x)}{\arcsin(...
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1answer
1k views

How can I calculate area enclosed by three curves in WolframAlpha?

I'm trying to calculate the region enclosed by $y=\frac{1}{x^2}$, $y=x$ and $y=4$ for $x \in [\frac{1}{2}, 4]$ How can I do this? I know I can use definite integral for this task but I want a general ...
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0answers
44 views

How to find multifactorials $ n\underbrace{!!\ldots !}_m$ in Wolframalpha?

I heed to compute $ n\underbrace{!!\ldots !}_m$. The formula is $ n\underbrace{!!\ldots !}_m = \prod_{i=1}^{k}(mi-r)$, $n=3m-r$, $k \in Z$, $r \in \{0,1,\ldots, m-1\}$. Question. Is it exist a ...
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0answers
146 views

Right-to-left cycle multiplication in Wolfram alpha

Wolfram alpha carries out cycle multiplication from left-to-right. If the context dictates a right-to-left (function composition) operation, there probably is a way (short of rearranging the order of ...
2
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1answer
53 views

Solving $(x^3 -3x)^2 = x+2$: is this a problem with WolframAlpha?

$f(x)=(x^3 -3x)^2 - x-2$ Well, I was trying to find the roots of this polynomial of degree $6$ and, after a look at WolframAlpha I noticed something strange. According to Wolfram, there are $3$ real ...
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1answer
78 views

The Diophantine equation system

I deal with the following equation system: $$k \left(k^4+5 k^2 m+5 m^2\right)=1 \\ k^2+4 m=l^2$$ Mathematica and Maple show that the solution of this system for the ${k,m}$ pair can not be ...
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0answers
96 views

Let Wolfram Alpha evaluate function for natural numbers only [duplicate]

How can I tell Wolfram Alpha that I only want it to evaluate my function for natural numbers? For example $ 2n $, assuming n integer used to work, but not anymore. Is there a new syntax I can use? ...
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1answer
328 views

Evaluating a 'WolframAlphan' integral

This problem has to be the real and integral part of Christmas... :) Here goes: What is the minimum value of $k$ such that $$\Re\left\{\int_{e^{\large 1/\pi}}^{\pi^{\large 1/e}}\left[% \left(\...
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1answer
38 views

Digamma function and asymptotic bounds

Knowing that $m\to \infty$, $n\to \infty$, $m^2<n^{2/3}$, I came across the following expression: $$\frac{2x^2}{\frac{x^2m^2}{n^{2/3}}+m^4n^{2/3}}$$ Playing a bit with said expression, I saw it ...
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3answers
186 views

Wrong Wolfram Alpha result for $\lim_{(x,y)\to(0,0)}\frac{xy^4}{x^4+x^2+y^4}$?

I'm trying to solve this limit: $$ \lim_{(x,y)\to(0,0)}\frac{xy^4}{x^4+x^2+y^4} $$ Here's my attempt: $$0 \le |\frac{xy^4}{x^4+x^2+y^4} - 0| = \frac{|x|y^4}{x^4+x^2+y^4},$$ and since $x^4+x^2 \ge0$...
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2answers
86 views

WolframAlpha wrong evaluate: $\lim\limits_{x \rightarrow a}\frac{x^m - a ^m}{ x^n-a^n}$

Let $a \in \mathbb{R}$ and $m,n\in \mathbb{N}$. If i let evaluate WolframAlpha this: $\lim\limits_{x \rightarrow a}\frac{x^m - a ^m}{ x^n-a^n}$ i get $\frac{ma^{m-n}}{n}$. In my opinion this is not ...
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1answer
204 views

Can I blindly trust WolframAlpha?

Recently, my friend gave me the following indefinite integral to evaluate : $$\int \frac{\sin^2 x }{\sin x +\cos x} \mathrm dx$$ I searched it on WolframAlpha, just to be sure, that whether it has an ...
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2answers
42 views

Convert the double integral into polar

$$\int^{4}_{0}\int_{0}^{\sqrt{4x-x^2}}\sqrt{x^2+y^2}\text{ dy dx}=14.22$$ In polar, we have $0\leq y\leq \sqrt{4x-x^2}$ Simplying, we get $y^2=4x-x^2$, which turns into $(x-2)^2+y^2=4$. Here is the ...
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2answers
2k views

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)}{\...
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1answer
44 views

Using RowReduce in Wolfram-Alpha gives wrong answer

I tried to check whether the vectors [1,1,1],[4,3,2],[3,1,6] are linearly independent over GF(7). I used "rowreduce([[1,4,3],[1,3,1],[1,2,6]]) in gf(7)" in Wolfram-Alpha and it told me they're ...
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0answers
61 views

Sum dependant on another sum

I want to calculate the sum: $$\sum_{k=1}^{1000} \frac{\lambda_1^k\exp(-\lambda_1)}{k!}(1-\sum_{n=0}^{k-1} \frac{1}{n!}exp(-\lambda_2 x)(\lambda_2 x)^n)$$ Wolfram Alpha seems to be having trouble ...
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0answers
128 views

How to convert a formula to discrete values in wolfram-alpha?

I don't know where this question fits, whether it is the right place... I plotted the Logistic Function $y=\frac{0.8}{1 + e^{-(x-6)}}$ using wolframalpha, here. Now I want to make it discrete, so I ...
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1answer
47 views

Software to do a jacobian matrix of four variable

I have to compute the jacobian wrt $\phi,\lambda_1,\lambda_2,\sigma$ of $C^S(\mathbf{h,x_0})=\sigma\sqrt{\mathbf{h^t\Sigma_{x_0}^{-1}h}}$ where: $$\mathbf{\Sigma_{x_0}=\Psi_{x_0}\Lambda_{x_0}\Psi_{...
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2answers
327 views

Diagonalizing 2x2 Matrix and Finding Eigenvalues of 2x2 Matrix yields different results in Wolfram. Why?

I want to find the eigenvalues of the matrix, $$ \begin{bmatrix} 0 & cos(k)+sin(k) \\ cos(k)+sin(k) & 0\\ \end{bmatrix}.$$ With diagonalize {{0, cos(k)+sin(k)}, {cos(k)+sin(k)...
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1answer
217 views

How calculate one side limit with WolframAlpha? [closed]

I read examples, and try: lim ln(x+1) as x->inf from the left but always wolfram alpha represent infinity as positive.
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0answers
56 views

Why here is crooked line in $\log(\frac{a+1}{c+1})$ contour plot?

I plotted contour plot of this formula by Wolfram Alpha $$\log(\frac{a+1}{c+1}), 0 < a < 1000, 0 < c < 1000$$ the contour plot of the above formula In the above figure, there is a ...
3
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1answer
292 views

Plot multiple functions with log axis on Wolfram Alpha

I want to plot two functions on the same graph using a log y axis on Wolfram Alpha, but I can't find a way to do this. I've tried things like ...
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0answers
30 views

Identity Result Failure [closed]

I'm trying to enter an equation into Alpha, to see for which values this identity holds ...
-1
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1answer
91 views

Laplace transform does not work [closed]

I tried to use Laplace transform for this expression using Wolfram Alpha : $3.297\times10^9s^{-2.327}+1480$, but even Wolfram cannot do this... Why ? Thank you very much !
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0answers
61 views

How to solve $x$ for an equation with $x$ as an exponent and an argument of a logarithm?

I have the following equation: $$2^{-\frac{1}{x}}+1=-\log_2\left(\frac{1}{x}-1\right)$$ I can't find a way to solve it. I got it by the function $f(x)=\frac{1}{1+2^{-\frac{1}{x}}}$ when I was ...
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0answers
93 views

Validity of argument in dilogarithm identities on Wolfram

I've come across a series of identities existing between dilogarithms and powers of logarithms but I am not sure about when such equations are valid in terms of the restriction of the domain of the ...