linear algebra
by ay19bme, Jun 5, 2025, 11:17 AM
Approximate the integral
by ILOVEMYFAMILY, Jun 5, 2025, 5:27 AM
Approximate the integral
using the trapezoidal rule with accuracy
.
![\[
I = \int_0^1 \frac{(2^x + 2)\, dx}{1 + x^4}
\]](http://latex.artofproblemsolving.com/e/3/9/e391d4208a008146dc3922ff31ac1f544172b5b4.png)

This post has been edited 1 time. Last edited by ILOVEMYFAMILY, Yesterday at 9:38 AM
3xn matrice with combinatorical property
by Sebaj71Tobias, Jun 1, 2025, 6:33 AM
Let"s have a 3xn matrice with the following properties:
The firs row of the matrice is 1,2,3,... ,n in this order.
The second and the third rows are permutations of the first.
Very important, that in each column thera are different entries.
How many matrices with thees properties are there?
The answer for 2xn matrices is well-known, but what is the answer for 3xn, or for kxn ( k<=n) ?
The firs row of the matrice is 1,2,3,... ,n in this order.
The second and the third rows are permutations of the first.
Very important, that in each column thera are different entries.
How many matrices with thees properties are there?
The answer for 2xn matrices is well-known, but what is the answer for 3xn, or for kxn ( k<=n) ?
The matrix in some degree is a scalar
by FFA21, May 20, 2025, 12:11 AM



Is it true that


This post has been edited 1 time. Last edited by FFA21, May 20, 2025, 12:07 PM
Another integral limit
by RobertRogo, May 9, 2025, 2:28 PM
Let
be a function differentiable at 0 with
. Find




On units in a ring with a polynomial property
by Ciobi_, Apr 2, 2025, 2:21 PM
We say a ring
has property
if :
a) Prove that if a ring
has property
, and
are distinct elements, such that
and
are units, then
is also a unit, but
is not a unit.
b) Provide an example of a ring with property
.


![\[
\begin{cases}
\text{the set } A \text{ has at least } 4 \text{ elements} \\
\text{the element } 1+1 \text{ is invertible}\\
x+x^4=x^2+x^3 \text{ holds for all } x \in A
\end{cases}
\]](http://latex.artofproblemsolving.com/b/6/9/b6993ee76eb3792e08d441f5d5c463247c392c4a.png)







b) Provide an example of a ring with property

Infinite series with Pell numbers
by Entrepreneur, Nov 5, 2024, 12:55 PM
Evaluate the sum
Where
denotes the n-th Pell Number given by
and 




Derivatives on a Functional Equation
by Kingofmath101, Jun 4, 2017, 6:03 PM
Let
be a smooth function on
where
for all
and
satisfies

for all
. Prove that
for all
.






for all



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