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

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