For questions related to usage of Wolfram Alpha.
1
vote
1answer
83 views
Am I right or is Wolfram right?
Let ${a_n}$ be a sequence whose corresponding power series $A(x)=\sum_{i\geq 0}a_ix^i$ satisfies
$$A(x)=\frac{6-x+5x^2}{1-3x^2-2x^3}$$
Determine a recurrence relation that ${a_n}$ satisfies.
I ...
4
votes
1answer
33 views
Polar coordinations - problem with r and $\theta$
let's take a look on Archimedean spiral.
the polar equation is $r = \theta$. click here to look.
but $\tan (\theta) = y/x$ and $r = \sqrt{x^2+y^2}$,
so $r = \theta \rightarrow \tan(\sqrt{x^2+y^2}) ...
0
votes
2answers
30 views
Series expansion with remaining $log n$
I'm studying the asymptotic behavior $(n \rightarrow \infty)$ of the following formula, where $k$ is a given constant.
$$ \frac{1}{n^{k(k+1)/(2n)}(2kn−k(1+k) \ln n)^2}$$
I'm trying to do a series ...
0
votes
1answer
97 views
Mathematica vs Wolfram Alpha integration results
When I insert the following integration command in wolframalpha:
...
0
votes
0answers
26 views
Phase Shifting Equations Wolfram
I'm working on testing different phase shifting equations and solving for $\phi$ each time I come up with a new set is starting to get troublesome. I was looking at Wolfram Alpha and was wondering if ...
0
votes
0answers
28 views
Strange results for solving boundary angle of full reflection
I was trying to solve the following group of equations for $\alpha$ using Wolfram|Alpha:
$$\frac{v_2\cdot\sin(\alpha)}{v_1} = 1 \\
v_1 > 0 \\
v_2 > 0$$
I expected something like $\alpha = ...
4
votes
1answer
57 views
Why doesn't $ \lim_{(x,y)\rightarrow(0,0)} xy\sin(\frac{1}{xy}) $ exist?
I've tried to get the following limit:
$$ \lim_{(x,y)\rightarrow(0,0)} xy\sin\left(\frac{1}{xy}\right) $$
wolfram claims it doesn't exist.
How to show that?
Why can't I take $z=xy$ and receive a ...
1
vote
1answer
98 views
Numerical values of the Jacobi elliptic function sn: Wolfram Alpha vs. Maple vs. C++?
I have a problem to check the validity of an algorithm I've implemented in C++ to compute the Jacobi elliptic function $\mathrm{sn}(u, k)$ (inspired and improved from Numerical Recipes 3rd edition). I ...
0
votes
1answer
75 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
2answers
57 views
How to solve this graph problem in WolframAlpha?
I need to input this problem in WolframAlpha:
Write an equation of the line containing the given point and parallel to the given line: $(8,-8)$, $7x+8y=5$.
The answer is $7x+8y=-8$ but I'm not ...
0
votes
1answer
57 views
What does a dot after a number mean?
So I'm making some calculations for numerical analysis and the output I get in Wolfram or Mathematica for input like:
...
12
votes
5answers
478 views
The last few digits of $0^0$ are $\ldots0000000001$ (according to WolframAlpha).
Can anybody explain how this comes about?
1
vote
4answers
92 views
Wolframalpha - how to get value of function in a specific point?
For example , given this function -
$f(x) = x^3-x^2-x-1$
and I want to check it in the point $x=1.6$.
What should I have to write in the command line of wolframalpha in order to get it ?
1
vote
3answers
58 views
Generating function with quadratic coefficients.
$h_k=2k^2+2k+1$. I need the generating function $$G(x)=h_0+h_1x+\dots+h_kx^k+\dots$$ I do not have to simplify this, yet I'd really like to know how Wolfram computed this sum as ...
-2
votes
1answer
107 views
Entering roots into wolframalpha [closed]
I couldn't find the answer to this, then worked it out, so here it is.
To enter cubed root into wolfram alpha:
X^(1/3) as pointed out by MvG
Or into the app:
^3√X
0
votes
1answer
49 views
How to calculate vector * matrix-inversed in Wolfram Alpha?
I am trying to calculate the product of a vector and an inversed matrix in wolfram alpha:
$\begin{bmatrix}1 & 2 & 3\end{bmatrix}$ * $\begin{bmatrix} -0.5 & 0 & 0 \\ 3 & 1 & 0 ...
0
votes
1answer
89 views
Getting weird integral evaluation from Wolfram Alpha
Check this out. I hand-evaluated this integral and my pretty sure the answer is zero, but Wolfram returns the value $4i\pi$ instead.
0
votes
1answer
28 views
Permutations - bug in Wolfram Alpha?
I've got question whether Wolfram Alpha has bug in showing permutations. Check permutation rules, list, and two-line notation in this permutation.
I'd expect same result as was on Wolfram Alpha blog ...
1
vote
2answers
152 views
Wolframalpha step-by-step of $\int\frac{\cos(x)}{\sqrt{2+\cos(2x)}}dx$
I wonder, where the minus sign goes after the first $u$-substitution of integral $\displaystyle\int\frac{\cos(x)}{\sqrt{2+\cos(2x)}}dx$?
5
votes
4answers
300 views
Why WolframAlpha Result is Different?
http://www.wolframalpha.com/input/?i=x%3D10%5E-15%3B+%28e%5Ex-1%29%2Fx
When i click Approximate Form in result, the result is:
...
4
votes
5answers
110 views
Find the second derivative of $e^{x^{3}}+7x$
$$e^{x^{3}}+7x$$
Here is what I have tried so far,
$$y'=(e^{x^{3}})'+(7x)'$$
$$y'=3e^{x^{2}}e^x+7$$
$$y'=3e^{x^{3}+x}+7$$
I am supposed to find the second derivative but I believe I have already made ...
0
votes
2answers
224 views
How to enter subscript characters in WolframAlpha? [closed]
I'm trying to enter equations like this in WolframAlpha.
How do I format this?
0
votes
1answer
59 views
Equation with 2 variables tricky problem
So let's say I have some random equation $6yx^3 - 3yx + 5 = 0$, but could be anything.
How would I go about finding a value for $y$, that makes it so that this equation only holds true if $x$ is ...
16
votes
4answers
642 views
Wrong Wolfram|Alpha limit?
I have this function:
$$ f(x,y) = \frac {xy}{|x|+|y|} $$
And I want to evaluate it's limit when $$ (x,y) \to (0,0)$$ My guess is that it tends to zero. So, by definition, if:
$$
\forall \varepsilon ...
0
votes
2answers
422 views
Wolfram Alpha: How to define constants in a system of equations?
I'd like to use WA to solve a small system of nonlinear equations, that involve both constants and the variables of interest. How do I "tell" WA which variables are the constants, and which are the ...
1
vote
1answer
88 views
Moving the negative out of the integral - a bug in Wolfram Alpha?
A guy I follow on Twitter seems to be having some issues with Wolfram Alpha - namely that moving a negative outside of an integral results in two different answers:
$\int -f(x) = -\int f(x)$ gives ...
25
votes
4answers
706 views
A limit wrong using Wolfram Alpha
I want to calculate the following limit:
$$\displaystyle{\lim_{x \to 0} \cfrac{\displaystyle{\int_1^{x^2+1} \cfrac{e^{-t}}{t} \; dt}}{3x^2}}$$
For that, I use L'Hopital and the Fundamental Theorem ...
0
votes
1answer
27 views
How to calculate HarmonicNumber(x, 1.6)?
I got this solution while using Wolframalpha:
$$
(-1.66667 n+1/2-0.133333/n+0.0208/n^3-0.0127573/n^5+O((1/n)^6))/n^1.6+2.28577
$$
Could somebody tell me this solution step-by-step?
I need to write ...
0
votes
1answer
284 views
WolframAlfa/Mathematica how to find function local maximum on interval
I have a polynomial function and i want to find it's minimum and maximum on a the interval [0, 5] with Wolfram Alphaa but i forgot the proper input.
I recall it went something like so: $x^4 + x^3 + ...
5
votes
4answers
148 views
Should $x=-2$ be included as an answer for $\frac{x^2+8x+12}{x^2+5x+6}>0$?
$$\frac{x^2+8x+12}{x^2+5x+6}>0$$
First of all while solving inequalities I need to check domain so in this case $$x^2+5x+6\neq0$$
$$x\neq-2,\ x\neq-3$$
Later on
...
2
votes
1answer
128 views
Circumference of the ellipse, elliptic integrals, and WolframAlpha
The arc length of a graph of a function $f(x)$ is
$$\mathcal{l} = \int_a^b \sqrt {1 + f'(x)^2} dx$$
If you choose $f$ to be a parametrization of the ellipse with $a=1, b=\frac{1}{2}$, i.e. $f(x) = ...
1
vote
1answer
125 views
Wolfram|Alpha Plotting multiple geometric objects
I am trying to use WoflramAlpha to plot several gemoetries at once. It works fine up to an extent but after I add three different geometries to draw it just says it doesn't understand and picks ...
2
votes
2answers
133 views
(Wolframalpha) this shouldnt give x=50?
This is my problem:
I need x or y for the triangle area that forms between the vertical axis(y) and the function y=100+2x where the area is equal to 2500.
so I used for condition to the linear ...
5
votes
1answer
210 views
Wrong Wolfram alpha result?
I have this function
$$
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 ...
-1
votes
1answer
315 views
Wolfram Alpha: Cannot use w as a variable? [closed]
When I try to use $w_1$, $w_2$, $w_3$ as variable names in the Wolfram alpha,
It always interprets them as watts or omega-1 constant.
Is there any solution for this?
I do need to use $w_1$, $w_2$, ...
21
votes
1answer
275 views
Iterated exponent of $i$
WolframAlpha seems to tell me that $e^{e^{e^{e^{e^{e^{e^{e^{e^{e^{e^i}}}}}}}}}} = 1$, see link. Is this just an error or is it for real? Adding one more $e$ to the bottom of the tower gives me the ...
3
votes
1answer
215 views
How can I construct a 2^63-gon with a straightedge and compass?
I entered 2^63 as a stand alone value at WolframAlpha. Among
the responses was a factoid that 'A regular 9223372036854775808-gon is constructible with a straightedge and compass.'
What is such a ...
0
votes
1answer
60 views
Confusion in the answers given by mathematica
When I typed in
6^-1 mod 49 in Wolfram|Alpha, it gave me an answer of 41. Link here
If I type the same thing as (1/6) mod 49 , I don't see 41 any more. Why is this happening ?Link here
A ...
1
vote
1answer
193 views
How to plot and shade on Wolfram Alpha?
Many Mathematica parameters don't work on Wolfram Alpha. I tried filling -> f which it does not recognize.
I am trying to plot a simple region bounded by $y = ...
4
votes
2answers
129 views
Is $2^{\log_2(-5)}$ defined?
As far as I know for $\log_2 x$ to be defined $x$ must be higher than 0. However when I enter $2^{\log_2(-5)}$ into wolframalpha it gives result $-5$. Is it mistake?
1
vote
1answer
1k views
Contour integration and wolfram
I am not sure if this is the right site to ask this question, but here it is:
Does Wolfram Alpha do contour integrals? If so how might I access that feature. Also, is there an online manual for ...
1
vote
1answer
79 views
Question on y axis of Gamma probability distribution
Afternoon.
I'm looking into using the Gamma (Erlang) distribution for a certain quantity that I need to model. I noticed by plugging in some values for the distribution parameters that the y axis ...
1
vote
1answer
59 views
Trivial transfiguration
I have $\frac{2ab}{ab-ac-bc+c^2}$. Of course it's $\frac{2ab}{c^2-ac-bc+ab}$ which is $\frac{2ab}{c^2-c(a+b)+ab}$ but for the latter Wolfram tells me it's not the same as $\frac{2ab}{ab-ac-bc+c^2}$. ...
2
votes
3answers
408 views
WolframAlpha blows simple substitution?
I am to find a formula for the n-th derivative of $$\frac{1+x}{1-x}$$ I came up with $$\frac{(-1)^{n+1} \times 2 \times n!}{(1-x)^{n+1}}$$
This seems right, but I noticed that WolframAlpha somehow ...
0
votes
1answer
266 views
How to calculate vertices of dodecahedron using W|A?
Can I calculate for example with wolfram alpha coordinates of vertices of dodecahedron?
I know coordinates of center point of dodecahedron (center of gravity) and the height of dodecahedron.
Thanks ...
2
votes
1answer
219 views
Is wolframalpha a good nonlinear optimization tool? [closed]
Also how do you restrict the domain to be integers in wolfram alpha?
0
votes
3answers
135 views
Why doesn't WolframAlpha factor my equation?
I entered in a simple-looking quadratic equation, expecting WA to factorize it for me, but then it gives me all this other stuff without the actual factors. The result is exactly the same as my input. ...
1
vote
2answers
1k views
Why does Wolfram Alpha handle $\log$ and $\ln$ the same?
I thought $\log(n)$ was like $100^x = n$ and $\ln(n)$ was $e^x = n$. But when I do $\ln(80)$, it gives me the answer for $\log$. Why is that?
0
votes
1answer
5k views
Taylor series expansion of arctan(x) around the point 0
This is actually a technical question about why I'm getting different results when trying to do the same thing using Maxima and WolframAlpha.
When I enter
expand arctan(x)
in WolframAlpha I ...
0
votes
1answer
234 views
Priority of parentheses and brackets in basic arithmetic.
Wolfram alpha is giving inconsistent results to this problem:
When I enter:
16÷2( 8-3(4-2) )+1
the result is 17.
When I enter:
16÷2[ 8-3(4-2) ]+1 the result is 5.
and
16÷2*[ 8-3(4-2) ]+1 brings ...
