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:

Attention Control

The capacity to manage one's focus and selective attention towards desired stimuli while ignoring distractions.

Working Memory

A cognitive system responsible for temporarily holding information available for processing, important for reasoning and the guidance of decision-making and behavior.

Deductive Reasoning

A logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true.

Attention Control

The ability to regulate one's focus, including sustaining attention on tasks and shifting attention when necessary.