Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$

Multiple Choice

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = \sqrt { x - 3 }$ .

A) $\frac { 1 } { 3 \sqrt { x - 3 } }$
B) $\frac { 1 } { 2 \sqrt { x - 3 } }$
C) $\frac { \sqrt { x - 3 } } { 2 }$
D) $\sqrt { x - 3 }$
E) limit does not exist