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

question 188

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } } , \mathrm { L } = \frac { 1 } { 2 } , \mathrm { c } = 2$ , and $\varepsilon = 0.3$

• A) \(\delta = 0.75\)
• B) \(\delta = 0.375\)
• C) \(\delta = 3\)
• D) \(\delta = 10\)

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Definitions:

Equation

A statement of the equality of two algebraic expressions.

Verify

To prove or confirm that something is true, accurate, or genuine, often through the examination of evidence or conducting tests.

Pair of Equations

Two equations that are solved together to find a common solution for their variables.

Verify

To confirm or validate the truth, accuracy, or authenticity of something.