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

question 101

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 $x _ { t } 0 < \left| x - x _ { 0 } \right| < \delta \Rightarrow | f ( x ) - L | < \varepsilon$ .
- $$f ( x ) = \frac { x ^ { 2 } + 4 x + - 21 } { x + 7 } , x _ { 0 } = - 7 , \varepsilon = 0.03$$

• A) \(L = 0 ; \delta = 0.03\)
• B) \(\mathrm { L } = - 6 ; \delta = 0.04\)
• C) \(\mathrm { L } = 4 ; \delta = 0.04\)
• D) \(L = - 10 ; \ \delta = 0.03\)