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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = 7 x ^ { 2 } , L = 175 , c = 5 \text {, and } \varepsilon = 0.5$$

A) $\delta = 0.00715$
B) $\delta = 0.00714$
C) $\delta = 4.99285$
D) $\delta = 5.00714$