jmays14
Horizontal asymptote of the function f(x)= 6x^3+17x^2528/2x^314x+321



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jmays14
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\[f(x) = 6x^3+17x^2528/2x^314x+321\]

jmays14
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can someone help me please

Callisto
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Horizontal asymptotes
\[=f(x) = \lim_{x \rightarrow \infty} \frac{6x^3+17x^2528}{2x^314x+321}=...\]

jmays14
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yes thats the problem

Callisto
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Divide both the numerator and denominator by x^3

Callisto
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And \[\lim_{x \rightarrow \infty} \frac{1}{x} =0\]

jmays14
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i got 3

Callisto
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Isn't it correct?!

jmays14
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what is the next step , i believe 3 is right

Callisto
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It is 3..

Callisto
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\[\lim_{x \rightarrow \infty} \frac{6x^3+17x^2528}{2x^314x+321}\]\[=\lim_{x \rightarrow \infty} \frac{\frac{6x^3+17x^2528}{x^3}}{\frac{2x^314x+321}{x^3}}\]\[=\lim_{x \rightarrow \infty} \frac{6+\frac{17}{x}\frac{528}{x^3}}{2\frac{14}{x^2}+\frac{321}{x^3}}\]Then take the limit