Find the Limit $L$ For the Given Function $f$ , the Point $x _ { 0 }$

Multiple Choice

Find the limit $L$ for the given function $f$ , the point $x _ { 0 }$ , and the positive number $\varepsilon$ . Then find a number $\delta > 0$ such that, for all $x _ { t } 0 < \left| x - x _ { 0 } \right| < \delta \Rightarrow | f ( x ) - L | < \varepsilon$ .
- $f ( x ) = m x + b , m > 0 , L = ( m / 8 ) + b , x _ { 0 } = 1 / 8 \text {, and } \varepsilon = c > 0$

A) $\delta = \frac { 8 } { m }$
B) $\delta = \frac { 1 } { 8 } + \frac { \mathrm { C } } { \mathrm { m } }$
C) $\delta = \frac { \mathrm { c } } { \mathrm { m } }$
D) $\delta = \frac { \mathrm { c } } { 8 }$