Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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-2
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0answers
28 views

What does meant notebook for wolfram demonstration? [closed]

I have got the below message from Elia Stiglier director of wolfram demonstration to make published paper online at wolfram demonstration, But really i don't understand what does meant notebook they ...
3
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1answer
54 views

Solving an integral with limits of polygamma functions

I've been trying to solve the following integral: $$I_n=\int_0^1\frac1x\ln^n(x)\ln^{8-n}(1-x)~\mathrm dx$$ for $n\in[2,6]$. It can be computed as a limit of derivatives of the Beta function: $$I_n=\...
-1
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2answers
59 views

Wolfram Alpha can plot an equation but not solve it

I'm trying to solve the equation $24.6347 \left(246.347 x + \sqrt{(246.347 x + 20)^2 + 1} + 20\right)^{-a} =\\ 30.2879 \left(-33.6532 x + \sqrt{x (1132.54 x - 20191.9) + 90001} + 300\right)^{-a}$ ...
0
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2answers
46 views

Why does WolframAlpha omit the $n=4$ and $n=8$ term in this Fourier series?

I tried to determine the Fourier series of the function: $$ f(x) = \begin{cases} x+\pi, & -\pi \le x < -\frac{\pi}{2} \\ \frac{\pi}{2}, & -\frac{\pi}{2} \le x <\frac{\pi}{2} \\ \pi-x, ...
3
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2answers
525 views

How does WolframAlpha solve quintic equations (5th degree polynomials)?

There exists no general formula for quintic equations. Then how does WolframAlpha solve quintic or higher degree polynomial. Is there a sure way to get values of roots of quintic or higher degree ...
1
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2answers
61 views

How do I solve a recurrence relation with multiple conditions?

Suppose I have a recurrence relation like : \begin{equation} f(n)=\begin{cases} 2*f(n-1) , & \text{n%2 = 1}.\\ f(n-1) + 1, & \text{n%2 = 0}. \end{cases} \end{equation} \begin{...
0
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2answers
4k views

What is $(-1)^X?$

Why the negative number raised to X gives strange graph? Y = (-1) / X This is sine and cosine both functions in real and imaginary part. How to explain this?
0
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1answer
34 views

Is there some technique to plot complex functions by hand?

Is there some technique to plot complex functions by hand? Particularly, consider e.g. $$x=\exp(t)\cos(t), y=\exp(t)\sin(t)$$ This is equivalent to $e^x(\cos(y)+i\sin(y))$ along line $y=x$, just ...
2
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0answers
59 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 ...
0
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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 ...
2
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1answer
100 views

A bug in Wolfram Alpha about an infinite series?

While verifying this MSE answer, I may have come across a bug in Wolfram Alpha. It evaluates the sum below as, $$\qquad A=\sum_{n=0}^\infty\frac{\binom{2n}{n}^2}{16^n(n+1)^3}=1.03928049\color{red}{51}...
1
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3answers
138 views

How to finds primes $p$ with the property that both $10p^2+9$ and $8p^2-9$ are also primes using Wolfram Alpha? [closed]

I want to know the number of primes $p$ that satisfies the condition that $10p^2 + 9$ and $8p^2 - 9$ are both primes, for primes $p$ only. How can I do it using Wolfram Alpha (or any other ...
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 ...
0
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1answer
38 views

How does one plot $z=(-2)^{3/5}$?

How does one plot $z=(-2)^{3/5}$? I see in Wolfram Alpha: https://www.wolframalpha.com/input/?i=z%5E5%3D-8 But I don't understand how that plot is created.
1
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4answers
111 views

Evaluating $\lim_{x \rightarrow +\infty} \frac{\sqrt x + x^3 -\sqrt{x^6-2x^4} -x}{\log(1+{e}^{3\sqrt x})}$

I'm trying to calculate the following limit: $$\lim_{x \rightarrow +\infty} \frac{\displaystyle\sqrt x + x^3 -\sqrt{x^6-2x^4} -x}{\displaystyle \log(1+{e}^{3\sqrt x})}$$ For WolframAlpha the result ...
3
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3answers
90 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 ...
1
vote
1answer
41 views

3D plot difference Matlab and Wolfram

I'm trying to plot the function $z = 6x^2 - 4x^2y^2$ in Matlab. The code I'm using for this in matlab is the one below, also the plot is shown: ...
2
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1answer
41 views

FFT from scilab is different than wolfram alpha [closed]

I am getting completely different values of FFT([1,2]) in scilab and Wolfram. I wondering what is going on and who is right. ...
0
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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^\...
0
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2answers
35 views

Why “is $f(x)$ an odd function?” does not work with this function?

We know that $f(x)$ is odd if $-f(x)=f(-x)$. The function is $$f(x)=\begin{cases}2x-1&\text{if $-2<x<0$},\\2x+1&\text{if $0\leq x\leq2$}.\end{cases}$$ (link) Now I want to know if $f$ ...
1
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1answer
981 views

is ${x^{2/3}}$ the same as ${\sqrt[3]{(x^2)}}$ or ${(\sqrt[3]x)^2}$? domain?

is ${x^{2/3}}$ the same as ${\sqrt[3]{x^2}}$ and ${(\sqrt[3]x)^2}$? and what is domain of $x$? Wolfram Alpha shows different results for ${x^{2/3}}$ and ${\sqrt[3]{x^2}}$ representations. Is domain ...
2
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2answers
44 views

Infinite sum and partial sum not equal in Wolframalpha

$$\sum_{n=0}^{\infty} |(-0.8)^n \theta(n)-(-0.8)^{n-1} \theta(n-1)|$$ $\theta(n) = 1$ for $n \geq 0$ and 0 otherwise. My attempt to calculate this summation numerically with Python yielded 10. To ...
0
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0answers
21 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?
7
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1answer
139 views

Integral of $\frac{1}{x\sqrt{x^2-1}}$

I am very confused by this. I know that the derivative of $\text{arcsec}(x)$ is $\dfrac{1}{|x|\sqrt{x^2-1}}$. However, if you plug in the integral of $\dfrac{1}{x\sqrt{x^2-1}}$ into wolfram alpha it ...
0
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2answers
47 views

Is Wolfram Alpha wrong? (trig identity)

I have the following identity $$ \sqrt{\cos(2x)\sec^4(x)}$$ I use the property $ \sqrt{a} \sqrt{b} = \sqrt{ab} $ which then yields $$ \sqrt{\cos(2x)} \, \sec^2(x) $$ However, Wolfram tells me ...
0
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1answer
42 views

How to find coordinates that split this arc into 3 pieces of equal length?

I need the $x$ coordinates of two new points that split an elliptical arc between 2 given points in quadrant I into 3 equal pieces. How can I get these coordinates? I want to use Wolfram but I can ...
2
votes
1answer
50 views

Different forms of Maclaurin expansion of $f(x,y) = \frac{1}{x+y}$

I am trying to use Taylor series to approximate the value of $f(x,y) = \frac{1}{x+y}$ for some code I am writing. Using WolframAlpha to quickly compute the Maclaurin series gives me: $$ \frac{1}{y} - \...
0
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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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2answers
52 views

How to find $\frac{146}7 \mod{7}$?

I understand that if $\gcd{(b,c)}=1$ then we can find $\frac{a}b\mod{c}$ by writing $$x\equiv \frac{a}b\mod{c}$$ $$bx\equiv a\mod{c}$$ then reducing $a$ and solving the modular equation by finding the ...
6
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1answer
78 views

Inconsistency of limits

Let $I_n(x)$ and $L_n(x)$ be the modified Bessel and modified Struve functions of order $n$, respectively. Assuming $x$ is real, I am interested in the following limit: $$ \lim_{x\to\infty} \frac{I_0(...
2
votes
3answers
50 views

How to compute $a\cdot \lim\limits_{n \to \infty}n?$

How to compute $$a\cdot \lim_{n \to \infty}n?$$ I think such an expression is not valid. Though $\lim\limits_{n \to \infty}n=\infty$, which is not a concrete real number, we can not put it into a ...
3
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1answer
147 views

Why wolfram alpha claimed that this $\sum_{n=1}^{\infty}\sin (\frac{n}{\sqrt{n!}}) $ is converge by test and in the same time is diverge?

I'm confused why wolfram alpha claimed that this sum $$\sum_{n=1}^{\infty}\sin \left(\frac{n}{\sqrt{n!}}\right) $$ is convergent by test criterion, and in the same time is divergent in result below ...
0
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2answers
36 views

Ability to generate a list of 3-digit numbers from a pool of digits in Wolfram?

I am attempting to generate a list of all possible 3-digit numbers that can be made by the numbers 1, 3, 5, 6, 7 and 9. I believe Wolfram should have the ability to give me a list, however, I am not ...
1
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2answers
79 views

Integral in Symbolab and WolframAlpha have different results

So Wolfram Alpha and Symbolab have different reuslt for this integral $\int \frac{x}{x+2}dx$. I done it myself and got result like Wolfram Alpha : $x-2\ln|x+2|$. Symbolab display this one: $x+2-2\ln|x+...
2
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5answers
47 views

Range of function $f(x)=x \sqrt{1-x^2}$

How to find range of this function, it looks easy but somehow I am not able to do that . What is more important to me is , why is wolframalpha unable to find the range , is it not a simple enough ...
3
votes
2answers
126 views

Solving $1^x+2^x+3^x=0$ equations…

Is it possible to solve for x this kind of equation? Since 1,2,3 are not multiples to each other I see a priori no possibility. $$1^x+2^x+3^x=0; x?$$ Computing this on Wolfram Alpha, for example, ...
1
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2answers
69 views

Are all values of $x$ solutions for $e^{2\ln(\sin(x))} = 1 - e^{2\ln(\cos(x))}$ in $\mathbb R$?

Does all values of $x$ in $\mathbb R$ satisfy equation: $$e^{2\ln(\sin(x))} = 1 - e^{2\ln(\cos(x))}$$ I am asking this, because by checking WolframAlpha solution there is an answer: (all values for $...
0
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1answer
42 views

Solving simple quadratic - Wolfram Alpha confusion?

I have the following quadratic $$(2\sqrt 2 - 2)x^2 + \sqrt8 x + (1+\sqrt 2)=0$$ Now the discriminant of this is $0$, so it has one real repeated root. A plot on Desmos confirms this. However, ...
0
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2answers
77 views

Simple Differential Equation in Matlab and Wolfram get two different answer?

I'm a beginner in using Matlab. if I have a DE like $$x'(t)=\frac{1}{\sin (2x)}$$ How I can Implement in Matlab to calculate just answer? I try dsolve like as: ySol(t) = dsolve(ode,cond) but ...
14
votes
4answers
25k 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? An example of what I want to do: $\binom{n}{k}\cdot p^k \cdot (1-p)^{n-k} = \frac{1}{\sqrt{n\...
0
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3answers
65 views

Calculating Fourier series of $\cos^2(t)$ gives unexpected result

As I understand it: $\cos^2(t)$ is even because it is a product of two even functions $\cos(t)$. The Fourier series and Fourier cosine series of an even function is the same link. So in the fourier ...
-1
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1answer
46 views

Wrong wolframalpha result, calculating Carmichael number?

I put to wolframalpha $3^{560}\pmod{561}$ and result should be $1$ ($561$ is Carmichael number), but result is $375.$ https://www.wolframalpha.com/input/?i=3%5E560mod561 Why this happens? I found ...
1
vote
1answer
464 views

Is Wolfram Alpha correct?

Given the attempted derivative at http://www.wolframalpha.com/input/?i=d%28a%28x%29+choose+b%28x%29%29%2Fdx, I believe the result from Wolfram Alpha is off by a factor of 2 or, at least I get a result ...
0
votes
1answer
53 views

How to make Wolfram Alpha give me a range of possible answers for an equation if the subject is assumed to be an integer?

I am trying to use Wolfram Alpha, and I am trying to get it to give me a range of possible answers for y=(391-x)/x, if y was an integer. However, there are two problems I face with this. The first is ...
0
votes
1answer
67 views

Prove that $\sum_{i=1}^n \frac{1}{\sqrt i} < 2 \sqrt n$ by induction - result doesn't match to wolfram alpha's result

According to wolfram alpha, this inequality isn't true for $n > 2$. My result says otherwise. Assuming that the inequality is true for $n+1$, $\sum_{i=1}^{n+1} \frac{1}{\sqrt i} < 2 \sqrt {n+1}...
13
votes
1answer
2k 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 ...
0
votes
0answers
24 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 ...
0
votes
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 ...
0
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1answer
35 views

Wolfram Alpha - FourierParameters not working with discrete fourier transform

I am trying to calculate the discrete fourier transform using the signal processing convention. The documentation gives the followng example: ...
2
votes
1answer
919 views

How to do reduce rows with Wolfram Alpha over certain set

If I want to row reduce a matrix: $$ \begin{matrix} 1 & -1 & 0 & 4 \\ 2 & -2 & 1 & 3 \\ 5 & -5 & 1 & 15 \\ \end{matrix} $$ ...