Questions tagged [wolfram-alpha]
For mathematical questions related to the usage of WolframAlpha.
698
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Why does a product of elements smaller than 1 converge 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 ...
- 3
1
vote
1
answer
90
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Ambiguous solution of Integral in Wolfram Alpha
Wolfram Alpha gave me a solution to an integration that needs consecutive substitution, where I do not understand how to make a definite decision on which function should be u and which du.
$$\int x \...
- 1,514
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1
answer
110
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0
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1
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60
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HessianMatrix (norm[2](x)) in Wolfram
I'm very new to Wolfram-alpha. I'm trying to compute the Hessian Matrix of ||x|| where x is a vector. I tried this command HessianMatrix (norm[2][x]) in mathematica 13 where I use Wolframalpha input ...
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5
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1
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Why does Wolfram Alpha give two different, inconsistent answers for sum of a matrix?
I would like to find out what $\sum_{r=1}^{n} \pmatrix{1 & -1 \\ 0 & 2}^r$ is equal to.
I have typed this expression into WolramAlpha twice and got a different answer each time, both ...
- 143k
2
votes
1
answer
97
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WolframAlpha syntax - evaluate series at a point
I am looking for syntax for WolframAlpha, which would evaluate a series at a given point. My goal is to have a sheet of practice exercises with links to solutions in WolframAlpha.
Example problem: ...
- 19.6k
2
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2
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49
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Steps WA used to simplify $\left( \frac{\cos \beta \sin \beta \cos\phi +\sin \beta}{\sin^2 \phi + \sin^2\beta \cos^2 \phi} \right)^2\cos \phi$
I have the following expression:
$$\left( \frac{\cos \beta \sin \beta \cos\phi +\sin \beta}{\sin^2 \phi + \sin^2\beta \cos^2 \phi} \right)^2\cos \phi$$
Wolfram Alpha yields a simplified form of this ...
- 173
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4
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Indefinite integral that Wolfram Alpha can't solve
Does anybody know the indefinite integral problems that Wolfram Alpha can not solve but human can solve by using elementary functions?
(The meaning of "solve" here is to represent primitive function ...
- 97.7k
3
votes
1
answer
110
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Why does Wolfram Alpha give a wrong answer to a linear ODE with constant coefficients?
This is very odd as it is a really simple ODE and the interpretation of the input seems correct, yet Wolfram Alpha produces rubbish:
$$x'' - 2x' + x = t, \quad x(0) = 1.$$
Wolfram Alpha claims that ...
- 2,116
18
votes
1
answer
407
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How does Wolfram find the closed form of numbers?
Introduction
I don't know if this question has already been asked (I didn't find it in the list of questions already asked) and I hope it won't be closed immediately since it's technically a question ...
- 5,154
2
votes
2
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Why does Desmos not plot $ \sqrt{\frac{(x+y)^2}{2}} = \sqrt{x^2+y^2} + \sqrt{2} $?
I am working on the following problem:
I need to find the points above the line $l:y=-x$ for which it holds that the distance to $l$ is $\sqrt{2}$ greater than the distance to the origin.
I worked out ...
- 5,299
0
votes
2
answers
202
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How to integrate to get sinh? (Wolfram Alpha)
I am currently trying to find the curve that a surfer makes in attempting to get to beyond where the waves break while a current pushes against him perpendicularly, and am using this post as help: ...
- 7,649
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2
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$\int_{|z| = 2 }\frac{4z^7-1}{z^8-2z+1} dz= ?$
Problem: Compute $\int_{|z|=2} \frac{4z^7 - 1}{z^8 - 2z + 1}dz$.
Attempt: I notice that if $w = z^8 - 2z + 1$ then $dw = 2 (4z^8 - 1) dz$ so $$I=\int_{|z|=2} \frac{4z^7 - 1}{z^8 - 2z + 1}dz = \frac{1}{...
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Contradiction occurred trying to calculate the value of $\sqrt{2}+Re\Bigl(^{10}\hspace{-1mm}\left(-\sqrt{2}\right)\Bigr)$ [closed]
Today I was trying to calculate the value of $\sqrt{2}+Re\Bigl(^{10}\hspace{-1mm}\left(-\sqrt{2}\right)\Bigr)$ (i.e., $\sqrt{2}$ plus the real part of the tenth tetration of the base $-\sqrt{2}$) up ...
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Conformal Maps of Quaternions
When we use the wolframalpha to plot a complex function, like
$$f \left( z \right) = e^z, \text{ } z \in \mathbb{C}$$
, the program show us the conformal map, that take vertical and horizontal lines ...
- 233
4
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1
answer
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Why do CAS struggle with $\int\frac{dx}{1+\sinh x}$?
$\int\frac{dx}{1+\sinh x}$ is a slightly annoying but still easily solved integral using a weierstrass substitution and PFD. I'm mainly referring to WolframAlpha, but I've seen other computer algebra ...
- 137k
18
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2
answers
893
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Trying to calculate a limit with a finite product and WolframAlpha disagrees with my logic.
I want to calculate
$$\lim_{N \to \infty} \prod_{j=1}^{N} \frac{2j}{N + j + 1} \,.$$
Here is my logic:
For the range of the product operator ($1 \leq j \leq N $) the inequality $2j < N + j + 1$ is ...
- 79k
4
votes
1
answer
166
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How to integrate $\int \frac{1}{\sqrt{x+1}-\sqrt{x+3}+\sqrt{x+5}}dx$?
How to integrate $$\int \frac{1}{\sqrt{x+1}-\sqrt{x+3}+\sqrt{x+5}}dx$$.
In my school life , I learnt how to integrate $$\int \frac{1}{\sqrt{x+a}-\sqrt{x+b}}dx$$ or $$\int \frac{1}{\sqrt{x+a}+\sqrt{x+b}...
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Plot a piece of a spherical shell - Wolfram Alpha website
I'd like to know how to plot a piece of a spherical shell $0.118<r<0.236$, $0<\theta<\pi$, $0<\phi<\pi/2$ by using the website Wolfram Alpha.
- 1,150
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How to obtain a recurrence relation for Taylor series coefficients?
Recently, I asked WolframAlpha to give me the first few terms in the Taylor series for a complicated (but well-behaved) function. It did so, but also provided a recurrence relation for the ...
- 4,603
4
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0
answers
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Wolfram wishlist: series of $\Gamma(z)$ in $z=-m$. Cycle index of symmetric groups.
I found out that Wolfram has a wish list of formulas it is researching.
The first point is "Series for the gamma function"
We are searching for general formulas for the series expansion of ...
3
votes
3
answers
221
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Desmos and Wolfram Alpha contradict: Is $|1+x| \ge 1 - |x|$ true for all $x$?
Is $|1+x| \ge 1 - |x|$ true for all $x$?
When I solve this problem myself, I solved that it's true for all $x$.
But when I put it into Desmos, I get this:
https://www.desmos.com/calculator/vgxm3q1fso,...
- 45.7k
1
vote
1
answer
65
views
Integration of the function derivative wrt the function
According to wolframalpha
$$ \int f'(x)df(x) = f'(x) f(x) + constant $$
I am trying to get the RHS, but alas... I tried to apply integration by parts and to apply it twice
- 19.6k
0
votes
2
answers
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$(x - \frac{\pi}{2}) (x - \frac{3\pi}{2})(2-tan(x)) $ does not share roots with $(x - \frac{\pi}{2}) (x - \frac{3\pi}{2})$. Why?
I was practicing for my trig test, and I came across this question $2\cos(x) - \sin(x) = 0$. I tried applying the trig identity $\tan(x) = \frac{\sin(x)}{\cos(x)}$ resulting in the following equation:
...
- 1,928
1
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2
answers
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Definite integral $\int_{-\infty}^\infty \int_{-\infty}^\infty \exp(-x^2 y^2) \; dx dy$?
The deceptively simple-looking double integral
$$ \int_{-\infty}^\infty \int_{-\infty}^\infty \exp(-x^2 y^2) \; dx dy
$$ is clearly finite, but both maple and Wolphram alpha gives the value $\infty$...
- 261k
1
vote
1
answer
301
views
Difference in differentiation between Mathematica and Wolfram Alpha
I am trying to differentiate this:
$$f(x)=e^{-x^2}$$
In Wolfram Alpha I get this:
$$-2x\,e^{-x^2}$$
But in Mathematica I get:
$$-2x\,e^{-x^2}\log(e)$$
Why the difference?
- 1,318
0
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1
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views
Discrepancy wolfram alpha and hand calculation of a gaussian integral
Wolfram alpha gives me the following result:
$$ \int_0^{+\infty} \frac{x^2\, e^{-a x^2}}{\sqrt{x^2 +m^2}}\, dx = \frac{\sqrt{\pi}}{4 a} U\Big(\frac{1}{2},0, a m^2 \Big)$$
and it does use the usual ...
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2
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0
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views
How do I find the constants in this differential equation that describes the time taken for a bubble to rise to the surface.
I'm trying to model the behaviour of bubbles in a water column as accurately as I'm able to, and I modelled a Differential equation using F = ma and a free body diagram. The equation of motion I ...
0
votes
0
answers
30
views
FindRoot error in NDSolve
I have two coupled differential equations as follows
\begin{eqnarray}
\frac{\partial }{\partial x}U[x,y] &=&2V[x,y], \notag \\
\frac{\partial }{\partial y}V[x,y] &=&V[x,y]U[x,y]+1,
\...
- 19
2
votes
2
answers
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views
Domain of $\frac{1}{x^{-1}}$
Why WolframAlpha and other online calculators compute $x\in \mathbb{R}-\{0\}$ (and not $\mathbb{R}$) as the domain of $\frac{1}{x^{-1}}$?
Since $\frac{1}{x^{-1}}=\frac{1}{\frac{1}{x}}=x$, is not the ...
- 155k
5
votes
2
answers
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Why Wolfram gives inconsistent result for: $\int_0^\infty \frac{e^{x-x^2}-e^{-x-x^2}}{x}~dx$
Why Wolfram gives inconsistent result for :
$$I=\int_0^\infty \frac{e^{x-x^2}-e^{-x-x^2}}{x}~dx$$
As shown in the picture below, the analytical integration gives $-i\pi$, but numerical integration ...
- 20.5k
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0
answers
65
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Rationality of artan(2/pi)
I was messing around on Wolfram Alpha and I saw that the conversion of arctan(2/pi) from radians to degrees was 32.48. Wolfram Alpha usually shows more decimal spaces, so I was wondering where this is ...
1
vote
2
answers
260
views
Does this Fourier Legendre series inverting $\frac65\frac{x^x}{x+1}-\frac35$ diverge or it is a software issue past $\approx 25$ series terms?
$\def\P{\operatorname P}$
The goal of the Fourier Legendre series is to find an exact explicit series solution to $x^x=x+1$, not just $x=a+b+c+\dots$ with unknown series coefficients. Lagrange ...
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2
votes
1
answer
76
views
How does Wolfram|Alpha derive direct formulas for $\sum_{k=0}^nk^m$? [duplicate]
I'm curious as to how Wolfram|Alpha manages to derive a direct formula for summations of powers, such as the classic $\sum\limits_{k=0}^n k^2$, or more difficult ones such as $\sum\limits_{k=10}^{n} k^...
- 3,226
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votes
4
answers
2k
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How to plot the polar equation theta = pi/6 on wolframalpha
I need to plot the polar equation
$\theta=\frac{\pi}{6}$
My question has two parts.
Is it a line? I'm pretty sure it is, since the angle theta in the polar equation is a constant, but since I was not ...
- 145
15
votes
3
answers
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views
Evaluate $\int_{-\infty}^\infty \frac{\sin{(x\sin{x})}}{x^2}dx$.
Evaluate $$\int_{-\infty}^\infty \frac{\sin{(x\sin{x})}}{x^2}dx.$$
Numerical investigation suggests that it equals $\pi$.
Let $f(\alpha)=\frac{1}{\pi}\int_{-\alpha}^\alpha \frac{\sin{(x\sin{x})}}{x^2}...
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0
answers
59
views
Wolfram Mathematica won't open Documentation Search
I was running a code I wrote and until some time everything was operational (using version 12.3). When I tried to revisit the same document after a while, it was not able to produce the same results ...
0
votes
1
answer
100
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How to evaluate $\displaystyle \int_0^{\frac{\pi}{2}}\ln(1+\sin(t)^2)\mathrm{d}t$ [duplicate]
I'm struggling with this integral, I've tried different substitutions but i can't solve it.
$$\displaystyle \int_0^{\frac{\pi}{2}}\ln(1+\sin(t)^2)\mathrm{d}t$$
I've tried to calculate both the ...
0
votes
1
answer
57
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Feeding parameters into a multivar function in Mathematica
I am trying to find an intersection point between a plane and a line. I defined my line as a function of $x,y$ and $z$.
g[x_, y_, z_] := 5 x - 8 y + 2 z - 13
I ...
- 137k
2
votes
0
answers
40
views
Wolfram says series is divergent, how is my proof wrong? [duplicate]
Given the following series Wolfram Alpha says it diverges but when I was trying to prove it I came to the conclusion it converges and I can't figure out what's wrong.
$$\sum_{n=2}^\infty \frac{(-1)^n}{...
- 21
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3
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Value of $x$ such that the area under the curve of $lnx$ up to $x$ is $1$.
This value would be the solution to:$$\int_{0}^{a}\ln(x)dx=1$$
With integration by parts this is well known to be $[x\ln(x)-x]^a_0=1$ or what is the same:$$a\ln(a)-a=1$$ The limit at $0$ easily ...
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2
votes
2
answers
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views
Can you help me understand the properties and zeros of this function involving square roots terms?
Consider this function ( I got this when I was solving an another problem)
f(n) =
$$\left(\frac{1}{2}\right)\left[\left(\frac{n^2+\sqrt{n^4+16008n}}{2n}\right)+\sqrt{\left(\left(\frac{n^2+\sqrt{n^4+...
- 76.5k
1
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1
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Closed form solution $\sum\limits_{n=1}^{\infty}\frac{\left(-1\right)^{n}}{H_n}$
$$\sum\limits_{n=1}^{\infty}\frac{\left(-1\right)^{n}}{H_n}$$
Where $H_n$ denotes the nth harmonic number.
I am a little confused because WolframAlpha says here that it is approximately $-0.626332$ ...
- 32.2k
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votes
1
answer
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views
Solve a 2D linear recurrence
I need to know the solution of this recurrence:
$$2a[n,k-1]-a[n-1,k-1]-2a[n-1,k-2]+a[n-2,k-2]=a[n,k]$$
With the initial value unspecified.
Also, wolfram is good at solving linear 1D recurrence, but ...
- 82k
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vote
0
answers
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PDF or CDF of the sum of two Weibull random variables with shape parameter 1/2
I saw that the pdf of the sum of two independent Weibull random variables is not known in general.
However, in the case of 'shape parameter = 1/2' in both variables, is there a closed-form expression ...
- 11
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votes
1
answer
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views
How can i use Maple(or any other software) to rearrange any equation into another equation? [closed]
Let's say I have some equation $= x^2+y=3$. I want to somehow rearrange this into something else such as $x=({\rm root}(3-y) z)/z$. I solved for x and multiplied z above and below. Can Maple (or some ...
- 5,293
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votes
2
answers
138
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Discrepancy in value of $\int_0^\frac\pi2 \delta(\tan(t)-xt)dt$
The goal would have been for the smallest positive solution of $y\cot(y)=x$ using a Dirac $\delta(x)$ Fourier series and the Bateman function:
$$y\cot(y)=x\mathop\implies^?\frac1{\sec^2(y)-x}=\int_0^\...
- 7,363
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1
answer
57
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Deriving CI for the mean: Wolfram Alpha giving different answer for equation and inequality [closed]
As a simple example, say I'm trying to derive the upper bound of a confidence interval for the mean. That is, I'm trying to solve for $\mu$ in
$$ \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} < Z_{\...
- 11.5k
2
votes
0
answers
170
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Wolfram Mathematica: why is the plot not visible?
simple question regarding Wolfram Mathematica:
Why is the plot not showing?
(See screenshot)
(I am new to Wolfram Mathematica)
Thankful for any input.
- 67
1
vote
0
answers
94
views
How are person curves created?
One can graph some person curves such as Joe Biden curve and Kim Jung Un Curve using WolframAlpha. I am curious how these curves were created using parametric equations.
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