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

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) $\delta = \frac { 0.05 } { m }$