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 $x _ { t } 0 < \left| x - x _ { 0 } \right| < \delta \Rightarrow | f ( x ) - L | < \varepsilon$ .
- $\mathrm { f } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 2 } , \mathrm {~L} = 243 , \mathrm { x } _ { 0 } = 9 \text {, and } \varepsilon = 0.5$

A) $0.00926$
B) $9.00925$
C) $0.00925$
D) $8.99074$