📘 higher mathematics

1. **Постановка задачі:** Знайти інтеграли за формулами, де $a=4$, $b=9$, $c=8$. 2. **Інтеграл 1:** $\int a \, dx = \int 4 \, dx$

1. **Problem:** Find the limit of the sequence \(\lim_{n \to \infty} \frac{1 + 4 + 7 + \dots + (3n - 2)}{\sqrt{5n^4 + n + 1}}\). 2. **Formula and rules:** The numerator is an arith

1. **Problem:** Verify if the matrix \( R = \begin{bmatrix} 2 & -3 & -5 \\ -1 & 4 & 5 \\ 1 & -3 & -4 \end{bmatrix} \) is a solution matrix or not. Since the problem is ambiguous wi

1. **Problem 1:** Find the value of $\theta$ if $\sqrt{2}$ is given and options are 45° or 90°. Since $\sqrt{2}$ is the length of the hypotenuse in a right triangle with legs of le