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The image appears to contain mathematical exercises written in Russian. Here's what I can extract and translate:

**TEST ЗПФ (TEST ZPF)**

1. Prove, based on the definition, that:
   \( \lim_{x \to 1} (2 - 4x) = -2 \)

   Answers:
   1) \( \delta = \frac{\varepsilon}{2}, \forall \varepsilon \)
   2) \( \delta = \frac{\varepsilon}{4}, \forall \varepsilon \)
   3) \( \delta = -\frac{\varepsilon}{4}, \forall \varepsilon \)
   4) Correct answer is not indicated.

It seems to be a limit problem where the answers provide conditions for \( \delta \)-\( \varepsilon \) reasoning related to the proof of the limit.

Would you like help solving the limit or discussing how to work with \( \delta \) and \( \varepsilon \) proofs for limits?

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Here are 5 questions to expand on the topic:

1. How is the concept of \( \delta \)-\( \varepsilon \) used to formally prove limits?
2. Can you find the limit using a direct substitution approach first?
3. How does the choice of \( \delta \) depend on \( \varepsilon \) in limit proofs?
4. What is the significance of proving limits using formal definitions rather than informal calculations?
5. Can you graphically interpret \( \delta \)-\( \varepsilon \) proofs?

**Tip**: When working with limits, always try direct substitution first before using more formal definitions.

Prove, based on the definition, that lim(x -> 1) (2 - 4x) = -2

Explore the process of proving the limit lim(x -> 1) (2 - 4x) = -2 using the formal epsilon-delta definition. This problem illustrates how to work with epsilon (ε) and delta (δ) to rigorously prove limits in calculus.

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