# Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

573 questions
Filter by
Sorted by
Tagged with
41 views

### Why Mathematica doesn't evaluate the derivative of the logarithm? [closed]

I'm trying to compute the second-order derivatives of the negative log likelihood as follows: $$P(t) = \int_{0}^{t}p(v)dv\\ \mathcal{L}(t)=-\eta_n\log\left(1-P(t)\right)\\$$ Where $P(t)$ is the CDF ...
26 views

### Is there a way to plot separate functions in 3D using Wolfram Alpha?

Is there a way to plot separate functions in 3D using Wolfram Alpha? Am I doing something wrong? Similar problem with GeoGebra
37 views

### Why are $e^{-4\ln(-x)+4}$ and $e^{-4\ln(-x)}$ positive?

Algebraically, why is $e^{-4\ln(-x)+4}$ a positive result but $e^{-4\ln(-x)}$ a positive result? It seems like with logarithmic properties, they should both be negative, but Wolfram Alpha shows the ...
29 views

### Software for evaluating summation expressions involving Stirling numbers of the first kind.

I know that for a summation such as $$p=\sum_{n=o}^{k}{\binom{k}{n}}=2^k,$$ Wolfram Alpha and some other computational software can easily tell that indeed the above summation evaluates to $2^k$. I ...
24 views

### Matrix representation after change of basis

I am trying to solve this task using Wolfram Notebook. I would like to know how new matrix is calculated (part b) after a change of basis. Part a: I decided to show this part because part b is a ...
34 views

### Solving a seemingly-trivial trigonometric equation for a specific variable

I'd like to express $y$ in $y = \sin (x*y)$. I can get $x = \frac{\arcsin y} y$ without any issues and then kind of don't know how to continue. WolframAlpha seems to have struggles with the equation ...
44 views

### Wolfram: doing substitution on indexed terms

I have sx = Sum[Indexed[x, i], {i, 1, 10}]^2 // Expand It expands in sum of 55 terms, from which $x_i^2$ - 10 terms, actual representation: $x_1^2+x_2^2+x_3^2+...$...
40 views

35 views

### Double series with WolframAlpha where the series are interdependent

How can be written a double series with WolframAlpha where the series are interdependent like, for instance, the following ones? $$\sum_{j=1}^i \sum_{i=2}^n (i^2-j)$$ (I don't get, as expected, a ...
65 views

### What's going on with this Wolfram Alpha matrix multiplication?

I was computing the matrix exponential of $$X = \begin{pmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{pmatrix}$$ by diagonalization. Wolfram Alpha and Symbolab both ...
25 views

81 views

### What are the mathematical steps used to get this $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$?

I have accrossed this representation in cubic sum $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$ at this website but am confused how mathematicains proved this , Now Is this ...
84 views

### Why does $\tan\left(\frac{1}{x}\right)$ look different to what I expect it should look like on WolframAlpha as x approaches 0?

https://www.wolframalpha.com/input/?i=tan%281%2Fx%29%2C+-0.01+%3C+x+%3C+0.01  https://www.wolframalpha.com/input/?i=tan%281%2Fx%29%2C+-0.001+%3C+x+%3C+0.001  For larger intervals of x, ...
65 views

59 views

58 views

### What is this method of solving called and why does it work? (From WA)

Wolfram Alpha uses a scary-looking algebraic method to solve $x^{3}-x-1=0$ that I've never encountered before. It seems that every other online algebra calculator uses numerical methods, such as the ...
539 views

### Computer tools to solve linear system of equations with singular matrix

According to the theory I've read, if $A$ is singular, the equation $A\vec{x}=\vec{b}$ will have either zero or infinitely many solutions. I tried solving this equation for: A=\begin{bmatrix} 4 &...
44 views

### Find the leading digit(s) of a factorial

What are the better methods (algorithms) to computing the first number (or few leading numbers) of a large factorial. Wolfram alpha seems pretty fast and handles large numbers. Is it accurate? Does ...
89 views

### How to calculate the area of a polar curve in Wolfram Alpha?

I know I can use plot polar r = cos(3theta), theta from pi/6 to -pi/6 to plot the polar curve of a equation, but I would like to check if my math is correct when calculating the area inside the curve. ...