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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = m x + b , m > 0 , L = \frac { m } { 5 } + b , c = \frac { 1 } { 5 } , \text { and } \varepsilon = c > 0$$

A) $\delta = \frac { c } { 5 }$
B) $\delta = \frac { c } { m }$
C) $\delta = \frac { 5 } { m }$
D) $\delta = \frac { 1 } { 5 } + \frac { c } { m }$