anonymous
  • anonymous
Horizontal asymptote of the function f(x)= 6x^3+17x^2-528/2x^3-14x+321
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[f(x) = 6x^3+17x^2-528/2x^3-14x+321\]
anonymous
  • anonymous
can someone help me please
Callisto
  • Callisto
Horizontal asymptotes \[=f(x) = \lim_{x \rightarrow \infty} \frac{6x^3+17x^2-528}{2x^3-14x+321}=...\]

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anonymous
  • anonymous
yes thats the problem
Callisto
  • Callisto
Divide both the numerator and denominator by x^3
Callisto
  • Callisto
And \[\lim_{x \rightarrow \infty} \frac{1}{x} =0\]
anonymous
  • anonymous
i got 3
Callisto
  • Callisto
Isn't it correct?!
anonymous
  • anonymous
what is the next step , i believe 3 is right
Callisto
  • Callisto
It is 3..
Callisto
  • Callisto
\[\lim_{x \rightarrow \infty} \frac{6x^3+17x^2-528}{2x^3-14x+321}\]\[=\lim_{x \rightarrow \infty} \frac{\frac{6x^3+17x^2-528}{x^3}}{\frac{2x^3-14x+321}{x^3}}\]\[=\lim_{x \rightarrow \infty} \frac{6+\frac{17}{x}-\frac{528}{x^3}}{2-\frac{14}{x^2}+\frac{321}{x^3}}\]Then take the limit

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