The image you uploaded contains a question asking to select the correct formulation of the theorem on the limit of intermediate sequences ("Теорема Предела промежуточной последовательности"). This is typically referred to as the Squeeze Theorem or Sandwich Theorem in English.

Correct Answer:

The fourth option from the list is the correct formulation of the Squeeze Theorem. It states:

• Let two sequences $\{a_n\}$ and $\{b_n\}$ converge such that $\lim_{n \to \infty} a_n = a$ and $\lim_{n \to \infty} b_n = a$, and if a third sequence $\{c_n\}$ satisfies $a_n \leq c_n \leq b_n$ for all $n \geq n_0$, then the sequence $\{c_n\}$ also converges, and $\lim_{n \to \infty} c_n = a$.

This is the correct mathematical expression of the Squeeze Theorem.

Do you want more details or have any questions?

Here are 5 related questions you might find helpful:

1. Can you explain how the Squeeze Theorem works in terms of inequalities?
2. How do you apply the Squeeze Theorem in a real example?
3. What are some common mistakes when using the Squeeze Theorem?
4. How is the Squeeze Theorem used in multivariable calculus?
5. Can you compare the Squeeze Theorem with other limit theorems?

Tip: The Squeeze Theorem is especially useful when dealing with sequences or functions that are difficult to evaluate directly but are "trapped" between two simpler limits.