For questions related to usage of Wolfram Alpha.

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1
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1answer
14 views

Does this Diophantine inequality have any solutions for $p, q \in \mathbb{N}$?

Does this Diophantine inequality have any solutions for $p, q \in \mathbb{N}$? $$p^2 q^2 \geq 3 p^2 q + 3p^2 + 3pq^2 + 3pq + 3p + 3q^2 + 3q + 3$$ I tried to use Wolfram Alpha, and it says that ...
1
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3answers
63 views

$0^0$ is undefined, but sometimes defined as $1$?

When typing a calculation to Wolfram Alpha it always takes $0^0$ as undefined, but for some calculations I need to preform, I specifically need it to be equal $1$. Is there a way to make it ...
0
votes
1answer
24 views

True or false under several conditions [closed]

I want to check whether $$\max\bigl(0, x+\max(0, y+z-1)-1\bigr)=\max\bigl(0, z+\max(0, x+y-1)-1\bigr)$$ under restriction $x,y,z\in[0,1]$ but I don't know how to type it in WolframAlpha. For example ...
-1
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2answers
58 views

Plot the solution curves of $\frac {dx} {dt} = - xe^{-x^2}$

Plot the solution curves and phase portrait of $$\frac {dx} {dt} = - xe^{-x^2}$$ It seems that it's increasing for $x < 0$ and decreasing $x > 0$. Then it seems concave down for $\frac {-1} ...
6
votes
3answers
1k views

Why is wolfram alpha plotting this differently?

I have an equation for a cylinder as $x^2+(y-b)^2=a^2$ for some $a$ and $b$. so I just plugged in $b=2$ and $a=1$ and tried to plot it using wolfram alpha, and the 3D plot looked like half a cylinder, ...
4
votes
1answer
68 views

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

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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1answer
25 views

Plotting numbers in the complex plane using WolframAlpha

I read this article on understanding imaginary numbers as rotations of real numbers in the complex plane. Having read it, it's easy for me to see how the real number $1$ is simply a point on the real ...
0
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0answers
10 views

Two variants of Radiality centrality

I am implementing Radiality centrality. For formula I am using definition from CentiScaPe: Network centralities for Cytoscape. I was doing some tests and I found some examples at Wolfram Alpha site. ...
0
votes
0answers
30 views

use of wolfram in determining area between two curves

I am new to the use of Wolfram (that for the limited cases I have used is very impressive). However I wonder if anyone can tell me what I am doing wrong. I wanted to calculate the area between the two ...
1
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1answer
25 views

Problem Inputting Formula Into Wolfram Alpha [closed]

I am trying to calculate the following: $1-\sum_{k=0}^4\frac{\binom{2,500}{k}\binom{247,500}{8,500-k}}{\binom{250,000}{8500}}$ I am inputting this into wolfram alpha like this but I can't seem to ...
0
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4answers
81 views

Is $x=0$ a local minimum of $f(x)=x^{2/3}(5-x)$?

It seems to be decreasing for values below zero and increasing for values between zero and 2. However $f'(0) = \frac{(-5 (x-2))}{3 x^{1/3}}|_{x=0}$ does not exist. So it's not a local minimum? Btw, ...
0
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1answer
14 views

PrimeQ[ Table[sum_(n=1)^(N)n!, {N,1,30}]]

The PrimeQ[Table[...]] command used to work in Wolfram|Alpha back in 2012 but now it doesn't give any answer. Is there a substitute?
0
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1answer
32 views

Partial derivative of $\frac{d}{dx}(x^2-2sin(y))$

WolframAlpha computes $\frac{d}{dx}\left(x^2-2(\sin y)\right)$ to be $$ \frac{d}{dx}\left(x^2-2 (\sin y)\right) =2 \left(x-(\cos y)y'(x)\right) $$ entered "differentiate (x^2 - 2*sin(y)) with ...
0
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0answers
27 views

Evaluating a sum on binomial coefficients

I'm reading Casella's and Berger's Statistical Inference. On page 239 they gives a claim that $$\sum_{x=0}^{330}\binom{300+x-1}x\left(\frac{1}{2}\right )^{300}\left (\frac{1}{2}\right )^x\approx ...
0
votes
1answer
48 views

Two results for the same (?) derivative $f(x) = \frac{y}{x}$

I was looking for a method to differentiate $f(x) = \frac{y}{x}$. Entering "differentiate $f(x) = y/x$" into WolframAlpha gives result: $$ f'(x) = \frac{-y}{x^2} $$ The main step of computing this ...
0
votes
1answer
71 views

Is wolframalpha wrong (Plotting inequalities)

I just wanted to plot a simple inequality: $$-x \geq 4$$ and wolframalpha gives me the following plot: But I think it should look like this: Am I correct? If so why is wolframalpha producing such ...
1
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2answers
40 views

Residue at infinty, contradiction?

I am trying to find the residue at $z=\infty$ of the function $$f(z)=\frac{z^4}{\sqrt{z^2-1}}$$ This has a Laurent series about $\infty$ of: $$f(z)= Z^3+ ...
1
vote
3answers
53 views

How do I tell Wolfram Alpha that I want the fourth derivative of y in a differential equation?

For example, how would I enter y^(IV) - 16y = 0? typing out fourth derivative, and putting four ' marks does not seem to work.
0
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1answer
40 views

Wolfram Alpha Step By Step For Systems of differential equation

Does anyone know if wolfram alpha has step by step solutions for systems of differential equations? When I input them, it comes up with an answer but it does not give me the step by step solution. I ...
6
votes
4answers
165 views

How many values does $\sqrt{\sqrt{i}}$ have?

Wolfram says, there are only two roots, but $\sqrt{i}$ already gives two roots. So if we express them in Cartesian form we can take square roots of them separately and end up with four roots. ...
1
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2answers
22 views

Integral of $-4\sin(2t - (pi/2)) $ weird behavior on wolfram alpha

I'm confused by what Wolfram Alpha is doing with my function: $$-4\sin{(2t - (\pi/2))}$$ on why the it gets replaced by $$4\cos{(2t)}$$. Is it equal? Link: See behavior here
3
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1answer
61 views

Repeating decimal notation of 1/53 on WolframAlpha vs notation on Wikipedia

WolframAlpha shows for 1/53 $0.0\overline{1886792452830}$ as the repeating decimal. Why is it not $0.\overline{0188679245283}$ instead? For example, Wikipedia shows for 1/81 ...
1
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1answer
34 views

Relations between hypergeometric functions

I am trying to find a relation between hypergeometrics $${}_2F_1(a,b,c;z)\,\,\text{and}\,\,{}_2F_1(a+1,b+1,c+1;z)$$ I can see that $$\frac{\partial}{\partial z}{}_2F_1(a,b,c;z) = ...
0
votes
0answers
12 views

Inserting “holes” on a graph.

I am trying to plot the set $A = \big\{(x,y) \in \mathbb{R}^{2} \mid x^{2} + y^{2} < 2 \big\} - \big\{(0,\frac{1}{n}) \mid n=1,2,3 \dots \big\}$. I have tried different combinations of set ...
1
vote
0answers
55 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
32 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 ...
0
votes
2answers
46 views

Calculating limits with Wolfram|Alpha

in a random graph setting with $n$ vertices and edge-probability $p$ I want to show that $\binom n4p^6\to 0$ as $pn^{2/3}\to 0$. To check this is even true, I submitted this Wolfram|Alpha query. Now ...
0
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0answers
66 views

Solid has same volume when axis of rotation increases?

I'm working on calculating the volumes of different solids using integration. The problem I'm working on says to find the volume of two solids, one revolved around the line $x = 4$ and the other ...
0
votes
2answers
38 views

About a solution in Wolfram Alpha

I'm intrigued by this finding on the extraordinary portal WolphramAlpha. What is the reason why the solution has not been simplified, eliminating the factor $\frac{\sqrt x \sqrt{x+2}}{\sqrt ...
1
vote
1answer
33 views

CAS based math program that can evaluate two sided limits? Ex:$\lim _{x\to 0}\left(\frac{1}{x}\right)=DNE$

I am new to Calculus and would like a CAS program to check my work without any hassles. I tried evaluating $\lim _{x\to 0}\left(\frac{1}{x}\right)$, a limit where the two sided limit DOES NOT EXIST in ...
7
votes
2answers
620 views

A ''strange'' integral from WolframAlpha

I want integrate: $$ \int \frac{1}{\sqrt{|x|}} \, dx $$ so I divide for two cases $$ x>0 \Rightarrow \int \frac{1}{\sqrt{x}} \, dx= 2\sqrt{x}+c $$ $$ x<0 \Rightarrow \int \frac{1}{\sqrt{-x}} \, ...
0
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0answers
18 views

Plotting standard deviation function using WolframAlpha

I'm trying to plot a standard deviation function using WolframAlpha's function plotter and my function looks like this: $SD(Y) = \sqrt{\sum_{i=2}^{k}\frac{k(i-1)}{ (k-(i-1))^2 }}$ where k goes from 1 ...
2
votes
1answer
62 views

Why is $\ln(\sqrt{|2x-5|}) + \frac{1}{2} \ln(|2x+3|) \neq \ln(\sqrt{|2x-5|}) + \ln(\sqrt{|2x+3|})$ in Wolfram Alpha?

According to Wolfram Alpha, $$\frac{1}{2} \ln(|2x+3|) = \ln(\sqrt{|2x+3|})$$ is always true, which makes sense given what I know of log rules. However, if I add the expression $\ln(\sqrt{|2x-5|})$ ...
3
votes
1answer
114 views

How does wolfram alpha compute this integral?

Wolfram alpha can find that $\int_1^\infty\frac{x^8-8x^7+24x^6-32x^5+19x^4-12x^3+17x^2-10x+2}{x^{12}-12x^{11}+56x^{10}-120x^9+82x^8+112x^7-182x^6-92x^5+381x^4-356x^3+170x^2-44x+5}dx=\frac{\pi}{2}$ ...
2
votes
2answers
76 views

Error on Matlab and Wolfram Alpha?

I solved the differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{y^2-1}{2y}$, in the following way: $\frac{\mathrm{d} y}{\mathrm{d} x}= \frac{y^2-1}{2y} <=>$ $\int ...
1
vote
1answer
73 views

How to calculate $\lim _{( x,y) \to (0,0) }\frac {x^2y^{3} }{\sin ( x^{8}+y^{4}) }$?

How to calculate $$\lim _{( x,y) \rightarrow (0,0) }\dfrac {x^2y^{3} }{\sin ( x^{8}+y^{4}) }$$ Wolfram Alpha says it is equal to $0$, but if calculate by trying $y=x$ then I get the limit $\lim ...
1
vote
1answer
65 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 ...
-1
votes
1answer
75 views

How to use Wolframalpha to verify the solution to a DE? [closed]

I would like to find the correct syntax for Wolframalpha so that it will test my solution to a DE. e.g. if I find that $y_p = -t^2 + \frac{3}{2}t - \frac{11}{8}$ and would like to see what that yields ...
1
vote
2answers
101 views

Floating point modulus precision (high multiple)

While looking at implementing floating point modulus in double-precision on an x86 CPU, I found the FPREM instruction and proceeded to test the practical precision in some cases, one being ...
1
vote
1answer
23 views

What doesn 2nd column depict in this table for perfect number description?

I am reading about perfect number at below link. http://mathworld.wolfram.com/PerfectNumber.html I am not able to understand what does the 2nd column (pn) depict? ...
0
votes
1answer
344 views

Can I get multivariable taylor series expansion on wolfram alpha or matlab?

I need something like this : say $a, x, y$ and $t$ are three non-negative real numbers. Now define the complex number, $z = -y + i(a+x-t)$ and consider the function $f(x,y) = z\text{ }tanh (\pi z) log ...
0
votes
1answer
45 views

How to find the number of solutions to an equation in wolfram alpha

Given the equation: $$sin(x)=\frac{x}{218}$$How do I use Wolfram Alpha to find the number of positive solutions?
1
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0answers
97 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). ...
6
votes
0answers
65 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 ...
1
vote
2answers
29 views

$\int_{c}^{c+2L} cos(\frac{2\pi nx}{L})$ Wolfram Alpha gives me this result but when doing I dont get it

$\int_{c}^{c+2L} cos(\frac{2\pi nx}{L}) = \frac{L sin(2\pi n) cos(\frac{2 \pi n(c+L)}{L})}{\pi n}$ dx with $n = 0,1,2,...$ I put this integral in Wolfram Alpha and gives me this result, but when I ...
0
votes
1answer
28 views

Solving system of equations

I'm trying to solve for $x$ and $y$ in the following system of of equations: $$((x-m)^2+(y-j)^2)(x-m)^2=((x-k)^2+(y-l)^2)(x-k)^2$$ $$((x-m)^2+(y-j)^2)(y-j)^2=((x-k)^2+(y-l)^2)(y-l)^2$$ I've tried ...
1
vote
2answers
100 views

Is there a reason to omit $[0]$ from the solution of the inequality $x^4 \ge x^2$?

This is the inequality I plugged in: $$x^4 \ge x^2$$ Wolfram Alpha gives me the correct number line, but the interval notation it gives me is missing $\{0\}$. (It gives me $(-∞, -1]$ and $[1, ∞)$, ...
2
votes
2answers
110 views

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 ...
0
votes
2answers
33 views

Augmented matrix gives no solutions when augmented with variables, but will give solutions when augmented with some numbers

I have a homework problem that boils down to this: x1 = 1a + 1b x2 = 1b + 1c x3 = 1c + 1d x4 = 1d + 1e x5 = 1e + 1f x6 = 1f + 1a I write the matrix to solve for x. I row-reduce the matrix. ...
4
votes
1answer
140 views

Calculating a sum which includes binomial coeffeicients

Some formula for calculating the probablity that the difference between the number $6$ and the average of accidentally selected $100$ points among $10000$ points which are distributed in the interval ...