Evaluate

ModifyingBelow lim With x right arrow infinity f left parenthesis x right parenthesislimx$$$$f$($x$)$

and

ModifyingBelow lim With x right arrow minus infinity f left parenthesis x right parenthesislimx$$$$f$($x$)$

for the following function. Then give the horizontal$$ asymptote$($s$)$ of f$($if any$).$

f left parenthesis x right parenthesis equals StartFraction $4$ x cubed plus $6$ Over $3$ x cubed plus StartRoot $36$ x Superscript $6$ Baseline plus $4$ EndRoot EndFractionf$($x$)=4$x$3+63$x$3+36$x$6+4$