Given That $\lim _ { x \rightarrow 3 } f ( x ) = 5 , \lim _ { x \rightarrow 3 } g ( x ) = 0 , \text { and } \lim _ { x \rightarrow 3 } h ( x ) = - 8 \text {, }$

Essay

Given that $\lim _ { x \rightarrow 3 } f ( x ) = 5 , \lim _ { x \rightarrow 3 } g ( x ) = 0 , \text { and } \lim _ { x \rightarrow 3 } h ( x ) = - 8 \text {, }$ find the following limits, if they exist. If a limit does not exist, explain why.(a) $\lim _ { x \rightarrow 3 } ( f ( x ) + h ( x ) )$ (b) $\lim _ { x \rightarrow 3 } x ^ { 2 } f ( x )$ (c) $\lim _ { x \rightarrow 3 } f ^ { 2 } ( x )$ (d) $\lim _ { x \rightarrow 3 } \frac { f ( x ) } { 2 h ( x ) }$ (e) $\lim _ { x \rightarrow 3 } \frac { g ( x ) } { f ( x ) }$ (f) $\lim _ { x \rightarrow 3 } \frac { f ( x ) } { g ( x ) }$ (g) $\lim _ { x \rightarrow 3 } \frac { 2 h ( x ) } { f ( x ) - h ( x ) }$ (h) $\lim _ { x \rightarrow 3 } \sqrt [ 3 ] { h ( x ) }$