Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of WolframAlpha.

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Proof of equality given by wolfram alpha

By 'playing' with wolfram alpha and entering this sum $$\sum_{n=0}^{+\infty}(-1)^n\left(\frac{1}{1+nx}+\frac{1}{x-1+nx}\right)$$ I found this alternative form that interest me: (since I don't know the ...
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-1 votes
2 answers
35 views

Solve basic system of equations with two unknowns. Why solution doesn't exists? [closed]

The following equation has no solution, but I'm not sure why exactly: $7 = 3x_1 + 5x_2 \\ 13 = (1 - x_1)3 + (1 - x_2)5 + 21$ Code for Wolfram Alpha ...
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Maximum of $\frac{Bx}{x^3 + Rx + P}$

I submitted this function to Wolfram Alpha and similar tools, but none can find for me the symbolic expression for maximum value, unless I give specific values to each parameter: $$\frac{Bx}{x^3 + Rx +...
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Numerical error in wolfram

In Wolfram Alpha, we see that $$\sum_{n=0}^\infty\frac{e^{-\pi^2n(n+1)}}{2n+1}=1$$ This is equivalent to $$\sum_{n=1}^\infty\frac{e^{-\pi^2n(n+1)}}{2n+1}=0$$ However, the last sum is impossible since ...
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Why is there a term $3.70074\times 10^{-17}x^2$ in this solution?

I was using WolframAlpha to find a polynomial of degree up to $2$ that best fits the points $(-1,2),(0,0),(1,-2),(2,-4)$. The answer I was expecting is $$0x^2-2x+0.$$ However, here is what ...
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2 votes
1 answer
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How to compute $ \sum_{x=y}^\infty \binom{x}{y}((1-p)(1-q))^x$?

Question How do I compute $ \sum_{x=y}^\infty \binom{x}{y} ((1-p)(1-q))^x$? $x,y$ are integers and $p, q \in (0,1)$ Attempt I'm trying to compute this sum to find the mixture of a geometric and ...
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  • 337
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Polar plot is different from rectangular plot

Here is a polar equation $r = \tan(\theta) $. I converted it into the rectangular form. This would be $$ \sqrt{x^2 + y^2} = \frac{y}{x} $$ When I plot both in ...
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  • 675
1 vote
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Nonsense matrix multiplication defaults in WolframAlpha

I just realized WolframAlpha arbitrarily decides which way to multiply matrices based on seemingly irrelevant stuff, and I'd like to understand whether the issue is with my knowledge of what's ...
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  • 111
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Find the maximum value of:$3\sqrt[3]{\dfrac{c^2-3a^2}{6}}-2\sqrt{\dfrac{a^2+b^2+c^2-ab-bc-ca}{3}}$

Let $a,b,c \in R$, find the maximum value of:$$3\sqrt[3]{\dfrac{c^2-3a^2}{6}}-2\sqrt{\dfrac{a^2+b^2+c^2-ab-bc-ca}{3}}$$ I have the solution: $$5a^2+2b^2+c^2-2(ab+bc+ca)=5(a-\frac{b+c}{5})^2+\frac{1}{5}...
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Restricting Domain in Wolfram Alpha for Nested Quantifiers

Is there a way to restrict the domain to all positive integers when you're using Resolve[] on nested quantifiers in Wolfram Alpha? If so, how? If not but there is ...
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4 votes
2 answers
287 views

Wolfram Alpha wrong Integral

I want to evaluate the following integral: $$\int_{-\infty}^0\frac{R}{\sqrt{x^2+R^2}^3}\mathrm{d}x$$ If I do it with the substitution $x=R\tan(\varphi)$ I get: $$\int_{-\infty}^0\frac{R}{\sqrt{x^2+R^2}...
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Wolfram alpha gives two different answers for $\int^{\infty}_{-\infty} x \frac{1}{\pi} e^{-(\ln(x) - 0.3)^2} | \frac{1}{x}|dx$

So, I'm trying to calculate $$\int^{\infty}_{-\infty} x \frac{1}{\pi} e^{-(\ln(x) - 0.3)^2} \left| \frac{1}{x}\right|dx$$ When I input that into WA, it loads for a bit, then shows this result: Just ...
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Matrix Power and Power Incorrect in Wolfram Alpha? [closed]

When computing the matrix \begin{bmatrix}1 & -\sqrt{3} \\ \sqrt{3} & 1\end{bmatrix} times its inverse, Wolfram Alpha produces this incorrect result. The same result happens when Power is ...
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4 votes
1 answer
143 views

Beth one equal to beth two not known?

Wolfram Alpha seems to say that ($\beth_1=\beth_2$) is unknown, but i'm pretty sure that $\beth_2$ is greater than $\beth_1$ ? is this just a bug in WA or is there a way in set theory that you can ...
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2 votes
1 answer
60 views

Is $\frac{\partial}{\partial x} \cos{\sqrt{x^2+y^2}}$ indeterminate or zero at (0,0)?

I'd like to know what's the derivative of $f(x,y)=\cos{\sqrt{x^2+y^2}}$ at $(0, 0)$. WolframAlpha says it is indeterminate. However, if we apply the definition, we can actually evaluate it to zero: $$ ...
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  • 369
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42 views

How do I find $\frac{\mathrm{d}}{\mathrm{d}x} \int_{x}^{\infty} f(t, x) \mathrm{d} t$?

I am trying to compute the following derivative: $$\frac{\mathrm{d}\Big(\int_{x}^{\infty} f(t, x) \mathrm{d} t\Big)}{\mathrm{d}x} \text{.}\tag{1}$$ It is straightforward to compute the following ...
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Wolfram Alpha computation of exponents

I am a bit confused by a Wolfram Alpha. In my calculations I had a term like $x^{(3/2)}$ which I wrote as $\sqrt{x^3}$. As silly mistakes happen quite often to me, I often double check stuff like this ...
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How to solve this system of equations in Wolfram Alpha?

I want to solve P0 + t0 * V0 + t2 * V2 == P1 + t1 * V1 for t0, t1 and t2, which are scalars, whereas the uppercase variables ...
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0 votes
1 answer
61 views

Can someone explain me what the limes of this example is? What does this solution of Wolfram mean?

This is the example I tried to solve with WolframAlpha. The result is also in the picture. Can someone explain me what the limes of this example is and how can i get there by hand? Limit[Power[(40)...
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3 votes
1 answer
128 views

Why is Wolfram's (presumably more precise) Maclaurin series a much worse approximation than my own (presumably less precise) series?

I recently answered this question, concerning the existence and nature of the implicit function defined by: $$F(x,y)=x^3-y^3-3xy+1$$ For $x$ close to $0$ - roughly the range $|x|\lt0.4$ - I showed how ...
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3 votes
4 answers
111 views

Getting the wrong value from $\lim_\limits{x\to-\infty}x-\sqrt{x^2+7x}$

Consider the following limit $$ \lim_{x\to-\infty}x-\sqrt{x^2+7x} $$ Going through some algebra leads to $$\begin{align} \lim_{x\to-\infty}x-\sqrt{x^2+7x}&=\lim_{x\to-\infty}\frac{(x-\sqrt{x^2+7x})...
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  • 3,676
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2 answers
55 views

Why does WolframAlpha give me an ugly graph for the input "(cos x-1)/x^2 when x=0.01"?

The function $\dfrac{\cos x-1}{x^2}$ is differentiable everywhere except for $x=0$. However, when I give WolframAlpha the input "(cos x-1)/x^2 when x=0.01", it gives me an ugly graph as ...
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  • 4,855
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2 answers
170 views

Graphing parametric equation software? Desmos/Mathematica/ other math software?

I want to view what the graph of, for example, $x=\sin t,\quad y = \sin(10t)$ looks like, but not as a static graph $\ y=f(x),\ $ but rather one where we can see the movement of the point on the $\ x-...
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1 answer
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Why does Wolfram Alpha give different answers to this algebraic equation depending on how it is entered?

I am trying to solve the equation $Ce^{-\sqrt L t} + De^{\sqrt L t} = Ce^{-\sqrt L (t + 2m\pi)} + De^{\sqrt L (t + 2m\pi)}$ for $L$. Here Wolfram Alpha returns the solution $m = \frac{in}{\sqrt L}$, ...
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3 votes
2 answers
179 views

Wolfram and Matlab show different Fourier Transforms for the function $H(z)=\sqrt{\frac{2}{\pi z}}e^{i\left(z-\frac{\pi}{4}\right)}$

I'm struggling with a discrepancy that Wolfram and Maple are giving me. To make everything comprehensible, I describe in the following what I did step by step. When I let Wolfram calculate the Fourier ...
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1 vote
2 answers
102 views

How to calculate the result of a recursive equation?

I'm looking for a tool (like Wolfram Alpha) that can calculate the result of $ B(P,N) $ Where $B(P,N)$ is a recursive function defined as follows: $ \left\{\begin{matrix} B(P,N)=\frac{-(-1)^{\frac{N}...
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1 vote
2 answers
241 views

Computing local and global minima on Wolfram Alpha

Consider $\sqrt{x^2+y^2}+2\sqrt{x^2+y^2-2x+1}+\sqrt{x^2+y^2-6x-8y+25}$. I need to find global or local minima of this function, but Wolfram Alpha doesn't seem to find one; the answer is that $1 + 2\...
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1 vote
3 answers
100 views

$e^{0\times I}$ in Wolfram Alpha broken?

How comes that $$ e^{0_2} = e^{\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}} = \begin{pmatrix}1 & 1 \\ 1 & 1\end{pmatrix} = 1_2 $$ according to Wolfram Alpha? Shouldn't $e$ to the power ...
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1 vote
2 answers
41 views

Quartic Circulant graph notation example

I would like to ask. I found the original image from Wolfram website and then cropped this example of circulant graph. Source: https://mathworld.wolfram.com/QuarticGraph.html Why does it says it is ...
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123 views

Wolfram alpha gives incorrect inverse function

I have trouble with Wolfram Alpha not fully calculating inverse of higher-order polynomial function. Function $$f(x)=3 x^6-5 x^4-4 x^2+8$$ (graph presented on a first photo Graph of $f(x)$) is not a ...
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5 votes
2 answers
256 views

Matrix exponential weirdness in WolframAlpha - it fails on diagonal matrices?

So Wikipedia says this, which makes sense: But Wolfram computed this: Is this a bug or am I just extremely tired?
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  • 8,561
4 votes
1 answer
142 views

What is the value of $\textstyle{{\sum\limits_{n=1}^{\infty}{\lim\limits_{u\rightarrow\infty}{\frac{(-1)^nu^{n+s}}{(n-1)!(n+s)}}}}}$?

First, I had put $\textstyle{\displaystyle{\sum_{n=1}^{\infty}{\lim_{u\rightarrow\infty}{\frac{(-1)^nu^{n+s}}{(n-1)!(n+s)}}}}}$ into wolfram alpha and got nothing. Then, I thought about inter-changing ...
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0 votes
0 answers
294 views

Why does Wolfram Alpha get this binomial coefficient sum wrong?

The sum I want to evaluate is $\sum_{i=2}^m \binom{p-1}{i-2} * \binom{n-k}{m-i}$. Here we have $p<k<=n$ and $m<=n$, all positive integers; I don't know how to communicate that to Wolfram ...
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0 votes
0 answers
37 views

Define start and stop for recursive formula

A recursive formula like a_{n} = a_{n-1}+4, how is it specified where to start and stop? In any computer language, I'd write something ...
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1 answer
211 views

Wolfram alpha plot of a piecewise function with 2 domains. [closed]

So, Wolfram Alpha is capable of plotting two functions in one figure. But I am trying to express a piecewise function that has a different form on two (touching) domains. In C code: ...
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2 votes
2 answers
107 views

Is $\frac{x^3}{x^2+y^4}$ continuous at (0,0)?

In an exam I was asked to determine if a function $f:\mathbb R^2\to \mathbb R$ is continuous at a point $(x_0,y_0)$, I needed to check if $$\lim_{(x,y) \to (x_0,y_0)} f(x,y) = f(x_0,y_0)$$ We consider ...
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0 answers
133 views

Specify choice variables and constants in Wolfram Alpha for maximisation

I seek to use Wolfram Alpha for some constrained optimisation problems, but I am unable to "tell" Wolfram Alpha, which of the symbols are variables (which ought to be chosen to maximise the ...
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3 votes
1 answer
54 views

$F(x,y)=(x^2,y)$ is not differentiable (According to WA), what am I missing?

Either wolfram alpha is getting crazy or I just completely misunderstood differentiability. Shouldn't it be enough for the partial derivatives to exist and to be continuous? Would the differential not ...
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1 vote
1 answer
58 views

Is the inequality $\sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t)$ false in general?

My question here is pretty basic: Is the inequality $\sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t)$ false in general? I tried asking WolframAlpha for its solutions, it says that no solutions exist. I ...
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1 vote
4 answers
135 views

$\lim_{z\to1}\frac{1-z^*}{1-z}$ using Wolfram Alpha

I wanted to verify the answer to many questions on limits of complex numbers. So, I tried using Wolfram Alpha for the same. $$\lim_{z\to1}\frac{1-z^*}{1-z}$$ does not exist. [using path $y=m(1-x)$] ...
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0 answers
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How to plot a skewed randon numbers on Wolfram Alpha, basically non-linear Ox axis?

I want to see Gauss' bell, but drawn over non-linear Ox axis. Basically i want to visually "catch" some asymetric and very rough plot, that hopefully is just a transformed normal ...
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0 votes
0 answers
30 views

Can Wolframalpha.com display the image of the map $(x,y,z) \rightarrow (x^{2}y,x-z)$?

I can do functions, like $f(x,y,z) = 1$. But is it possible to show the image of this morphism too; $(x,y,z) \rightarrow (x^{2}y,x-z)$?
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2 votes
1 answer
85 views

Maximise $(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)})^{\cos x}$

Maximise $$\large \left(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)}\right)^{\cos x}$$ I wonder why Mathematica says infinity as answer, but on desmos graph it is clear that it is less ...
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  • 1,126
0 votes
1 answer
84 views

Third vertex of equilateral SPHERICAL triangle

I’m trying to solve Fermat’s problem on sphere for the given triangle ABC using wolfram.I already made out,that in order to find a Fermat’s point i need to build three equilateral triangles on each ...
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0 votes
0 answers
29 views

Discrepancy in Wolfram Alpha for the domain of $(\log{x})^{-e^x}$

In my question Question I have discussed in the comments of the domain of $$(\log{x})^{-e^x}$$ In wolfram alpha as matter of fact the domain is $x\geq 1$, but I am not convinced of this fact since ...
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  • 343
0 votes
1 answer
31 views

Is it possible to use imaginary guesses with secant method?

I was playing with Wolfram Alpha today, and noticed that while I could use, say, $2i$ as a guess to solve $e^x+2=0$ with the help of Newton's method, I couldn't do the same with the secant method. Is ...
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1 vote
1 answer
145 views

Does every Matrix have a REF?

I'm wondering if anyone here has experience using Wolframalpha? I can't seem to get a row echelon form (REF) or echelon form, it always does reduced row echelon form (R-REF). Anybody know how to get ...
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  • 31
2 votes
1 answer
115 views

How does WolframAlpha calculate the power of 10 representation of a number? [closed]

Whenever I type some crazy big number on WolframAlpha, it outputs its power of 10 representation. For example, if I input $$ \large e^{6^{3643.23976}}$$ it outputs $$ \large 10^{10^{2834.629359002706}}...
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2 votes
0 answers
54 views

What does this slant "equals" sign indicate in this wolfram alpha plot?

When plotting the function $$\frac{(x^2 -1)}{(x^2 -x -2)}$$ with Wolfram alpha, the second plot has a slant "equals" sign right below when the graph hits the y-axis. What does this indicate? ...
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  • 325
1 vote
2 answers
687 views

Why wolfram doesn't plot the impulses for dirac delta function?

I give wolfram a Fourier transform to solve and I get my answer like this: but when I try to plot it using the plot command like this It doesn't plot the impulses given by the dirac delta function ...
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