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:

Health Expectancy

An estimate of how many years a person can expect to live in a state of good health by taking into account years lived in less than full health due to disease or injury.

Well-Years

A measure of the quality and length of life, quantifying the number of years lived in good health.

Life Expectancy

The average period that a person may expect to live, often used as a measure of the health and well-being of populations.

Disability-Free

The state of being without any physical or mental limitations that inhibit daily activities.