You Are Given $\lim _ { x \rightarrow a } f ( x ) = L$

question 26

Short Answer

You are given $\lim _ { x \rightarrow a } f ( x ) = L$ and a tolerance $\varepsilon$ . Find a number $\delta$ such that $| f ( x ) - L | < \varepsilon$ whenever $0 < | x - a | < \delta$ .
$$\lim _ { x \rightarrow 3 } 4 x = 12 ; \quad \varepsilon = 0.01$$

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Definitions:

Implied Authority

The power of an agent to act on behalf of a principal, derived from the actions, words, or conduct of the principal rather than from an explicit written or spoken agreement.

Express Authority

Authority explicitly granted by a principal to an agent to perform specific acts or functions on the principal's behalf.

Apparent Authority

Apparent authority refers to a situation where a person appears to have the agent's authority to act on behalf of another (the principal) due to the principal's actions, leading third parties to believe in the existence of such authority.

Manager

An individual responsible for controlling or administering all or part of a company or similar organization.