$(3$ pts for the open interval, $3$ points for $)$

$4.$ Find an open interval about $c$ on which the inequality $|f(x)-L|<mi></mi>$ holds. Then give a value for $>0$ such that for all x satisfying the inequality $|f(x)-L|<mi></mi>$ holds.

$f(x)=\sqrt[\phantom{2}]{x-7},L=4,c=23,=1$

$(13$ pts$)$ Prove the following limit statement by a delta epsilon proof: $\underset{x0}{lim}\sqrt[\phantom{2}]{4-x}=2$