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 $x _ { t } 0 < \left| x - x _ { 0 } \right| < \delta \Rightarrow | f ( x ) - L | < \varepsilon$ .
- $$\mathrm { f } ( \mathrm { x } ) = \frac { 10 } { \mathrm { x } } , \mathrm { x } _ { 0 } = 5 , \varepsilon = 0.1$$

A) $\mathrm { L } = 2 ; \delta = 0.53$
B) $\mathrm { L } = 2 ; \delta = 0.24$
C) $L = 2 ; \delta = 0.26$
D) $L = 2 ; \delta = 2.63$