Consider the Function $f ( x ) = \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 9 }$

Essay

Consider the function $f ( x ) = \frac { x ^ { 2 } - 8 x + 15 } { x ^ { 2 } - 9 }$ Make an appropriate table of values in order to determine the indicated limits:
(a) $\lim _ { x \rightarrow - 3 ^ { + } } f ( x )$ (b) $\lim _ { x \rightarrow - 3 ^ { - } } f ( x )$ (c) Does $\varliminf _ { x \rightarrow - 3 } f ( x )$ exist? If so, what is its value? If not, explain.