A Function $\mathrm { f } ( \mathrm { x } )$

question 265

Multiple Choice

A function $\mathrm { f } ( \mathrm { x } )$ , a point $\mathrm { c }$ , the limit of $\mathrm { f } ( \mathrm { x } )$ as $x$ approaches $\mathrm { c }$ , and a positive number $\varepsilon$ is given. Find a number $\delta > 0$ such that for all $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $f ( x ) = m x , m > 0 , L = 4 m , c = 4$ , and $\varepsilon = 0.05$

• A) \(\delta = 4 + \frac { 0.05 } { m }\)
• B) \(\delta = 4 - \mathrm { m }\)
• C) \(\delta = 0.05\)
• D) \(\delta = \frac { 0.05 } { m }\)

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Definitions:

Logical Operation

An operation in computational and digital systems that is based on binary inputs and yields a binary output, following logical principles.

Control Circuit

An electrical circuit designed to control the operation of a main power circuit, often used in applications like motor starts and stops.

Physical Connections

Refers to the tangible linkages or joints between two parts or components within a system.

Logical Connections

The connections between entities that are governed by logic, typically in the context of computer science and digital circuits.