Questions tagged [wolfram-alpha]
For mathematical questions related to the usage of WolframAlpha.
637
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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 ...
-1
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2
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35
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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
...
- 748
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1
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48
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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:
$$\frac{Bx}{x^3 + Rx +...
- 171
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1
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54
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Numerical error in wolfram
In Wolfram Alpha, we see that $$\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$$
However, the last sum is impossible since ...
- 7,419
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36
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Why is there a term $3.70074\times 10^{-17}x^2$ in this solution?
I was using WolframAlpha to find a polynomial of degree up to $2$ that best fits the points $(-1,2),(0,0),(1,-2),(2,-4)$. The answer I was expecting is
$$0x^2-2x+0.$$
However, here is what ...
- 4,855
2
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1
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54
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How to compute $ \sum_{x=y}^\infty \binom{x}{y}((1-p)(1-q))^x$?
Question
How do I compute $ \sum_{x=y}^\infty \binom{x}{y} ((1-p)(1-q))^x$? $x,y$ are integers and $p, q \in (0,1)$
Attempt
I'm trying to compute this sum to find the mixture of a geometric and ...
- 337
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1
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21
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Polar plot is different from rectangular plot
Here is a polar equation $r = \tan(\theta) $. I converted it into the rectangular form. This would be
$$ \sqrt{x^2 + y^2} = \frac{y}{x} $$
When I plot both in ...
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54
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Nonsense matrix multiplication defaults in WolframAlpha
I just realized WolframAlpha arbitrarily decides which way to multiply matrices based on seemingly irrelevant stuff, and I'd like to understand whether the issue is with my knowledge of what's ...
- 111
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Find the maximum value of:$3\sqrt[3]{\dfrac{c^2-3a^2}{6}}-2\sqrt{\dfrac{a^2+b^2+c^2-ab-bc-ca}{3}}$
Let $a,b,c \in R$, find the maximum value of:$$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}...
- 83
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1
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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 ...
4
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2
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287
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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:
$$\int_{-\infty}^0\frac{R}{\sqrt{x^2+R^2}...
- 242
1
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1
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80
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Wolfram alpha gives two different answers for $\int^{\infty}_{-\infty} x \frac{1}{\pi} e^{-(\ln(x) - 0.3)^2} | \frac{1}{x}|dx$
So, I'm trying to calculate $$\int^{\infty}_{-\infty} x \frac{1}{\pi} e^{-(\ln(x) - 0.3)^2} \left| \frac{1}{x}\right|dx$$
When I input that into WA, it loads for a bit, then shows this result:
Just ...
- 81
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1
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Matrix Power and Power Incorrect in Wolfram Alpha? [closed]
When computing the matrix \begin{bmatrix}1 & -\sqrt{3} \\ \sqrt{3} & 1\end{bmatrix} times its inverse, Wolfram Alpha produces this incorrect result. The same result happens when Power is ...
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1
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143
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Beth one equal to beth two not known?
Wolfram Alpha seems to say that ($\beth_1=\beth_2$) is unknown, but i'm pretty sure that $\beth_2$ is greater than $\beth_1$ ? is this just a bug in WA or is there a way in set theory that you can ...
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2
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1
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60
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Is $\frac{\partial}{\partial x} \cos{\sqrt{x^2+y^2}}$ indeterminate or zero at (0,0)?
I'd like to know what's the derivative of $f(x,y)=\cos{\sqrt{x^2+y^2}}$ at $(0, 0)$.
WolframAlpha says it is indeterminate.
However, if we apply the definition, we can actually evaluate it to zero:
$$
...
- 369
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1
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42
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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 ...
- 45
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0
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34
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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 ...
- 141
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41
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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 ...
0
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1
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61
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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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1
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128
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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 ...
- 8,561
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4
answers
111
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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})...
- 3,676
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2
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55
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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 ...
- 4,855
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170
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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-...
- 12.2k
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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}$, ...
- 1,666
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179
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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 ...
user736865
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2
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102
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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}...
1
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2
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241
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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\...
1
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3
answers
100
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$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
$$
according to Wolfram Alpha? Shouldn't $e$ to the power ...
- 497
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2
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41
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Quartic Circulant graph notation example
I would like to ask. I found the original image from Wolfram website and then cropped this example of circulant graph. Source:
https://mathworld.wolfram.com/QuarticGraph.html
Why does it says it is ...
- 4,202
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123
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Wolfram alpha gives incorrect inverse function
I have trouble with Wolfram Alpha not fully calculating inverse of higher-order polynomial function. Function $$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 ...
- 11
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2
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256
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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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1
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142
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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 ...
- 2,203
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294
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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 ...
- 134
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37
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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 ...
- 41
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211
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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:
...
- 103
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2
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107
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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)$$
We consider ...
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133
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Specify choice variables and constants in Wolfram Alpha for maximisation
I seek to use Wolfram Alpha for some constrained optimisation problems, but I am unable to "tell" Wolfram Alpha, which of the symbols are variables (which ought to be chosen to maximise the ...
3
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$F(x,y)=(x^2,y)$ is not differentiable (According to WA), what am I missing?
Either wolfram alpha is getting crazy or I just completely misunderstood differentiability.
Shouldn't it be enough for the partial derivatives to exist and to be continuous? Would the differential not ...
1
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1
answer
58
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Is the inequality $\sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t)$ false in general?
My question here is pretty basic:
Is the inequality $\sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t)$ false in general?
I tried asking WolframAlpha for its solutions, it says that no solutions exist.
I ...
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4
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$\lim_{z\to1}\frac{1-z^*}{1-z}$ using Wolfram Alpha
I wanted to verify the answer to many questions on limits of complex numbers.
So, I tried using Wolfram Alpha for the same.
$$\lim_{z\to1}\frac{1-z^*}{1-z}$$ does not exist. [using path $y=m(1-x)$]
...
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0
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18
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How to plot a skewed randon numbers on Wolfram Alpha, basically non-linear Ox axis?
I want to see Gauss' bell, but drawn over non-linear Ox axis. Basically i want to visually "catch" some asymetric and very rough plot, that hopefully is just a transformed normal ...
- 151
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0
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30
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Can Wolframalpha.com display the image of the map $(x,y,z) \rightarrow (x^{2}y,x-z)$?
I can do functions, like $f(x,y,z) = 1$. But is it possible to show the image of this morphism too; $(x,y,z) \rightarrow (x^{2}y,x-z)$?
2
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1
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85
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Maximise $(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)})^{\cos x}$
Maximise $$\large \left(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)}\right)^{\cos x}$$
I wonder why Mathematica says infinity as answer, but on desmos graph it is clear that it is less ...
- 1,126
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1
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84
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Third vertex of equilateral SPHERICAL triangle
I’m trying to solve Fermat’s problem on sphere for the given triangle ABC using wolfram.I already made out,that in order to find a Fermat’s point i need to build three equilateral triangles on each ...
0
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0
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29
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Discrepancy in Wolfram Alpha for the domain of $(\log{x})^{-e^x}$
In my question Question I have discussed in the comments of the domain of $$(\log{x})^{-e^x}$$
In wolfram alpha as matter of fact the domain is $x\geq 1$, but I am not convinced of this fact since ...
- 343
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1
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31
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Is it possible to use imaginary guesses with secant method?
I was playing with Wolfram Alpha today, and noticed that while I could use, say, $2i$ as a guess to solve $e^x+2=0$ with the help of Newton's method, I couldn't do the same with the secant method. Is ...
- 13
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1
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145
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Does every Matrix have a REF?
I'm wondering if anyone here has experience using Wolframalpha?
I can't seem to get a row echelon form (REF) or echelon form, it always does reduced row echelon form (R-REF).
Anybody know how to get ...
- 31
2
votes
1
answer
115
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How does WolframAlpha calculate the power of 10 representation of a number? [closed]
Whenever I type some crazy big number on WolframAlpha, it outputs its power of 10 representation.
For example, if I input $$ \large e^{6^{3643.23976}}$$ it outputs $$ \large 10^{10^{2834.629359002706}}...
- 123
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0
answers
54
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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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2
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687
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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
...
- 53