Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

6
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101 views

$\prod_{k=2}^n (k^2 - k)$: is WolframAlpha wrong?

I tried to find the product of $k(k-1)$ from $k=2$ to $n$. The partial product values should be 12 at 3 and 144 at 4. But it's showing the wrong partial product. What went wrong? Screenshot
6
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0answers
71 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 ...
6
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0answers
144 views

How wolfram defines injectivity?

I was looking for a fast way of getting which function is surjective and injective. So I tried to find such command in wolfram and surprisingly it says to me that $ln(x)$ is not injective. Link to ...
6
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0answers
2k 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 ...
4
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0answers
319 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
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0answers
322 views

On convolution and a possible bug in Mathematica/Wolfram Alpha

Let $f:\mathbb R_+\to\mathbb R_+$ be defined as $$f(x)=\frac 1{x^n}\text{u}(x)$$ where $n$ is a positive integer and $\text{u}$ is the unit step function. Define $g$ as the convolution of $f$ with ...
3
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0answers
72 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 $-\sqrt2 \mathsf{Mod}^{(1,0)}(0,\frac\pi2)$, ...
2
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0answers
57 views

Wrong Wolfram alpha result on $nth$ derivative?

I'm working with this function $$f(x)=\left(x+\sqrt{x^2-a}\right)^{-b}$$ and I would like to know the $nth$ derivative of $f(x)$. To this end, I ask Wolfram alpha about that given me the following ...
2
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0answers
107 views

How can I compute a fourier series with Wolfram alpha?

How can I compute the Fourier series of a function on a interval using Wolfram ? For example, the Fourier of $f(x)=x^2$ on $[0,2\pi]$ prolonged on $\mathbb R$ by $2\pi$ periodicity. For example, if I ...
2
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0answers
179 views

How can I restrict a variable to a given domain in Wolfram Alpha?

Ever since I began using Wolfram Alpha for quick online calculations I have had trouble specifying the domain of my variables. Note that I have already read the related MSO question "Tell Wolfram ...
2
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0answers
116 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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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 ...
2
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0answers
44 views

Complex exponentiation in Wolfram Alpha

I don't well understand how WA performs the exponentials in the complex field. I see that a simple case as $(-1)^{2/3}$ is treated as $((-1)^{1/3})^2$ so it gives (for the principal values): $$ (-1)^{...
1
vote
0answers
107 views

Why is $x \in \emptyset$ considered undetermined by WolframAlpha?

In an exercise, I had to prove, that the following statement is true: $A\setminus B = A \cap \bar{B}$ The task itself was not hard to solve, but I immediately had the question, if this statement ...
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0answers
36 views

How can I get solution to this partial differential equation using Wolfram Alpha?

Solve: $\frac{\partial ^3z}{\partial x^3}-4\frac{\partial^3z}{\partial x ^2\partial y}+\frac{\partial ^3 z}{\partial x \partial y^2}-2\frac{\partial^3z}{\partial y^3}=e^{2x+y} $ I want to get the ...
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0answers
165 views

Why WolframAlpha does LU decomposition with pivoting even when it isn't needed?

I want to do LU decomposition with $A$: $ A= \left[ {\begin{array}{cc} 1 & 2 & 3 & 4 \\ -9 & 8 & -15 & 4 \\ 2 & 13 & -21 & 7 \\ 4 & -5 & 5 ...
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0answers
32 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 ...
1
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0answers
33 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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0answers
60 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
79 views

WolframAlpha norm notation

I am having problems to understand the notation of a WolframAlpha result. Evaluating this equation, I am getting following: $$-4 \ ||-u + x||_2 \ (-z + ||-u + x||_2^2) \ \text{Norm}^{(1,0)}(-u + x, 2)...
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0answers
94 views

WolframAlpha Equation Solving: what do these solution conditions mean?

I used a WolframAlpha query to solve a problem relevant to some applied work I'm doing. The input interpretation box shows that WolframAlpha has correctly understood my input. Because I have the Pro ...
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0answers
29 views

What is the minimum $1 \pmod 4$ prime that satisfies this inequality?

Let $q \equiv 1 \pmod 4$ be a prime number. Define $\theta$ to be the real number $$\theta:=\dfrac{\ln(4/3)}{\ln(13/9)} \approx 0.782329851.$$ Here is my question: What is the minimum $q$ that ...
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0answers
108 views

What is wrong with my formulas for a mathematical model of a double pendulum?

I wanted to create a computer simulation on Matlab, using a model for a pendulum from this study (A double pendulum model of tennis strokes. Rod Cross. Uni of Sydney, 2006) - Link I wanted to use the ...
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0answers
464 views

How to graph 3D functions of two variables on Wolfram Alpha?

How to graph this on wolfram, google, or other free software: \begin{alignat*}{3} x(s, t) &= a\cos(mt) \cos^{k}(ns) &&\cos(t) &&\cos(s), \\ y(s, t) &= a\cos(mt) \cos^{k}(ns) &...
1
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0answers
33 views

Does y = 2 + 0(1/(x-2)) contain a hole? Seemingly no?

Out of curiosity, I typed the equation y = 2 + 0(1/(x-2)) into wolfram alpha to find that it simplified it to y = 2. Is this correct? I assumed there would be a hole or some lack of continuity at x = ...
1
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0answers
109 views

Maple and WolframAlpha return different results

I solved the integral of u/(1-u) by hand and found as result -ln(1-u) - u + constant. Now, when I evaluate this integral with WolframAlpha, I get the same result. But when I evaluate it with Maple, it ...
1
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0answers
318 views

Application of Initial Value Theorem

Let $$F(s):=\frac{s}{2s-i}$$ be the Laplace transform of some $f(t)$. I have been asked to compute $f(0^+)$ assuming that this quantity, intended as limit, exists. I thought I could apply the IVT ...
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0answers
114 views

A WolframAlpha error?

Consider the equation: $$ \dfrac{1}{\sqrt[3]{(x+3)^2}}-\dfrac{1}{\sqrt[3]{x^2}}=0 $$ that has the solution $x=\dfrac{-3}{2}$ as can be easely verified. But WolframAlpha gives no solutions (here). ...
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0answers
91 views

Why wolfram alpha find no solution to $x^\frac13= -1$?

Surely, $x=-1$ is the only solution. But, wolframalpha says there is no solution in the real field. I think this is because they transformed $x^\frac13$ to $e^{\frac 13(\ln x)}$. But why did ...
1
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0answers
101 views

Did Wolfram Alpha make this term up?

So I'm currently taking a Trigonometry class and I'm using the iOS version of the Wolfram-Alpha app to assist me with some of the more mundane calculations (Pythagorean Theorem, etc) and I've come ...
1
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0answers
100 views

radius of convergence of $1/\ln(in)$

I have series when $n$ goes from $1$ to infinity $(z/\ln(in))^n$ and need to find the radius of convregence. I tried this $1/R = \limsup ((1/\ln(in))^n)^(1/n)$ when $n \to \infty$ (Cauchy's rule), $1/...
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0answers
91 views

hypothesis test and execution? did I do this right?

I am trying to figure this out and I'm not sure if I am doing it right. a) did I select the correct type of hypothesis testing??? b) am I using the numbers in the right place (I have SD for 3.5 for ...
1
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0answers
155 views

Strange results for solving boundary angle of full reflection

I was trying to solve the following group of equations for $\alpha$ using Wolfram|Alpha: $$\frac{v_2\cdot\sin(\alpha)}{v_1} = 1 \\ v_1 > 0 \\ v_2 > 0$$ I expected something like $\alpha = \sin^...
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0answers
30 views

Why do these Residues and Numerically Calculated Contour Integrals Disagree?

I've been trying to numerically approximate various contour integrals of the function $f(z)=\frac{\sin\left(\pi x\right)}{\sin^2\left(\frac{15\pi}{x}\right)}$, but it seems that the residues and ...
0
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0answers
40 views

Plot a graph with a hole in Wolfram Alpha

I would like to emphasize graphs with holes in Wolfram alpha, so I've tried graphing a rational function with a hole. However, the graph that WA is generating isn't showing the hole. Is there a way to ...
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0answers
19 views

Numerical Double Integration with inverse over inner integral failing using common methods and inbuilt functions

Implementing a paper, I want the value of this double integral which has endpoint singularities in both integrals. $\int_0^{\inf} \frac{1}{w} Im( 0.5^{-iw}({12{\int_0^1 (1 - (0.5+\frac{0.5} {1+by^\...
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0answers
20 views

How to plot a Riemann sum in Wolfram alpha

I am wondering if there's a simple way to plot a function with a Riemann sum in Wolfram alpha. I've looked in a bunch of places for a tutorial but can't seem to find one. Anyone wanna help please?
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0answers
23 views

Calculating an area of parametric function with wolframalpha?

Using wolframalpha, how can I calculate an area between some parametric function like: $\begin{cases} x(t) = t^2 - t \\ y(t) = t^3\end{cases}$ and: some other function like: $y = x^2$ ? I've ...
0
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0answers
19 views

Wolfram Mathematica input form of conditional probability

I heard that the conditional probability form of Wolfram Mathematica is like this: Probability[x < 1 \[Conditioned] ....... However, what is Mathematica input form of double conditioned. For ...
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0answers
17 views

The first principal subresultant coefficient of two polynomials

Let $f=f(x), g=g(x) \in \mathbb{C}[x]$, with $\deg(f)=\deg(g)=n \geq 2$. Write $f=(x-a_1)\cdots(x-a_n)$ and $g=(x-b_1)\cdots(x-b_n)$, where $a_i,b_i \in \mathbb{C}$, $1 \leq i \leq n$. Let $\lambda,\...
0
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0answers
35 views

Computing subresultants in WolframAlpha

Let $f(x)=(x-a_1)(x-a_2)\cdots(x-a_m)$ and $g(x)=(x-a_{m+1})(x-a_{m+2})\cdots(x-a_n)$, where $m,n \in \mathbb{N}$, $m < n$, $a_i \in F$, $F$ is a field of characteristic zero (for example, $k \in \{...
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0answers
61 views

How to generate interpolating polynomial using Newton formula for exponential function?

I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0\ and\ x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division ...
0
votes
0answers
14 views

Using WolframAlpha to check cycle products for figuring out L/R cosets

I've been told and have noticed that WolframAlpha computes the order of elements a little differently than my class. How would I plug in multiple cycles so that I can check my work? I have noticed ...
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0answers
22 views

Reduction of appearing dilogarithms

I have a series of dilogarithms with various arguments and I was just wondering if it is possible to tell if they are all independent (that is to say, cannot be transformed into each other through e.g ...
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0answers
31 views

How to perform constraint optimization with undefined parameters in WolframAlpha?

I'm having trouble finding how to do a constraint optimization with undefined parameters in WolframAlpha. For example, how do I solve a standard Cobb Douglas problem such as: maximize $A x^a y^b$ on $...
0
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0answers
19 views

Approximation for fractional function for given boundary conditions

I try to find an approximation for the following expression $$\tan\phi(x)=\frac{\mathrm{si}(x)\sin(kx)-\mathrm{si}(x-\tau)\sin(k(x-\tau))}{\mathrm{si}(x)\cos(kx)-\mathrm{si}(x-\tau)\cos(k(x-\tau))} \...
0
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0answers
76 views

How to minimize or maximize a function over a finite field in WolframAlpha?

Is it possible to ask WolframAlpha to minimize or maximize a function with variables in a finite field? Let's take a stupid example: how do I ask WolframAlpha to maximize $x_1+x_2$ with $x_1, x_2\in\...
0
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0answers
51 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 ...
0
votes
0answers
92 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 ...
0
votes
0answers
43 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 ...