Evaluate lim f(x) and lim_x rightarrow -infinity f(x) lot the following rational

Question

Evaluate lim f(x) and lim_x rightarrow -infinity f(x) lot the following rational function. Use infinity of -infinity where appropriate. Then give the horizontal asymptote of f(if art) f(x) = 9x^2 - 9x + 8/3x^2 + 1 A. lim_x rightarrow infinity f(x) = B. The limit does not exist and is neither infinity nor -infinity. A. lim_x rightarrow -infinity f(x) = B. The limit does not exist and is neither infinity nor -infinity. Identify the horizontal asymptote. Select the correct choice below and if necessary, fill in the answer box to complete your choice.

Explanation / Answer

a)limx-> f(x)

limx-> (9x2-9x+8)/(3x2+1)

limx-> (x2(9-(9/x)+(8/x2)))/(x2(3+(1/x2)))

limx-> (9-(9/x)+(8/x2))/(3+(1/x2))

=(9-0+0)/(3+0)

=9/3

=3

b)limx->- f(x)

limx->- (9x2-9x+8)/(3x2+1)

limx->- (x2(9-(9/x)+(8/x2)))/(x2(3+(1/x2)))

limx->- (9-(9/x)+(8/x2))/(3+(1/x2))

=(9-0+0)/(3+0)

=9/3

=3

horizontal asymptote is y =limx-> f(x)

horizontal asymptote is y =3

and

horizontal asymptote is y =limx->- f(x)

horizontal asymptote is y =3

only one horizontal asymptote , i.e, y=3

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