anonymous
  • anonymous
find the limit of this please \[\lim_{x \rightarrow -infinity}(5x+12)/\sqrt{9x^2+x-3}\]
Mathematics
katieb
  • katieb
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myininaya
  • myininaya
\[\lim_{x \rightarrow -\infty}\frac{5x+12}{\sqrt{9x^2+x-3}} \cdot \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}\] now recall \[\sqrt{x^2}=|x|=x \text{ if } x<0 \] x<0 since we are approaching negative infinity so we have \[\lim_{x \rightarrow -\infty}\frac{5x+12}{\sqrt{9x^2+x-3}} \cdot \frac{\frac{1}{-x}}{ \frac{1}{\sqrt{x^2}}}\]
myininaya
  • myininaya
\[\lim_{x \rightarrow -\infty} \frac{-5+\frac{-12}{x}}{\sqrt{9+\frac{1}{x}-\frac{3}{x^2}}}\]
myininaya
  • myininaya
\[\frac{-5 +0}{\sqrt{9+0-0}}\]

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myininaya
  • myininaya
oops small type-0 |x|=-x if x<0
myininaya
  • myininaya
everything else is good
anonymous
  • anonymous
is the final answer -5/sqrt 9
myininaya
  • myininaya
the sqrt(9)=3
anonymous
  • anonymous
ok i see thanks again myininaya
myininaya
  • myininaya
np

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