anonymous
  • anonymous
I'm trying to find the limit when x->(-)infinity of (sqrt(x^6+3x^5+1)) / (7x^3+2x^5) what do i do with the sqrt in the numerator? is the answer infinity or sqrt(1)/7?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sqrt(x^6+3x^5+1)/(7x^3+2x^5)\]
anonymous
  • anonymous
\[\lim_{x \rightarrow -\infty} \sqrt{x^6+3x^5+1}/(7x^3+2x^5)\]
UnkleRhaukus
  • UnkleRhaukus
\[\lim\limits_{x\rightarrow-∞} \frac{ \sqrt {{x^6+3x^5+1}}} {7x^3+2x^5 }\]

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More answers

anonymous
  • anonymous
does the \[\sqrt{x^6}\] turn into \[x^3\]?
UnkleRhaukus
  • UnkleRhaukus
in the limit that x is large and negative the important terms are the \[\sqrt {x^6}\text{, and the }2x^5\]
anonymous
  • anonymous
but does the sqrt simplify to an x^3 or stay to the 6th power?
anonymous
  • anonymous
x^3 / 2x^5 ->low degree/high degree -> lim=0
anonymous
  • anonymous
or 6th power / 5th power -> high/low -> lim=infinity
UnkleRhaukus
  • UnkleRhaukus
yeah your right the \[√{x^6} \quad\text {would become}\quad x^3\] however x is negative so you cant do that
anonymous
  • anonymous
hmmm, so does the answer not exist?
UnkleRhaukus
  • UnkleRhaukus
um i am still trying to figure it out
anonymous
  • anonymous
okiedokie. take your time, this one has had me stumped for a long while...
UnkleRhaukus
  • UnkleRhaukus
i am just gonna use L'Hôpital's rule and see what happens
Zarkon
  • Zarkon
factor out an x^6 on the top and x^5 on the bottom
Zarkon
  • Zarkon
\[\frac{ \sqrt {{x^6+3x^5+1}}} {7x^3+2x^5 }\] \[=\frac{ \sqrt {{1+(3/x)+(1/x^6))}}} {x^5((7/x^2)+2)}\] \[=\frac{ |x^3|\sqrt {{x^6(1+(3/x)+(1/x^6))}}} {x^5((7/x^2)+2) }\] =...
Zarkon
  • Zarkon
limit will be zero
Zarkon
  • Zarkon
oops typo...
Zarkon
  • Zarkon
\[=\frac{ |x^3|\sqrt {{1+(3/x)+(1/x^6)}}} {x^5((7/x^2)+2) }\]
UnkleRhaukus
  • UnkleRhaukus
do not attempt to use L'Hôpital's rule, you wil run out of paper Zarkon has correct answer
anonymous
  • anonymous
oh, ok. So, when the x^6 gets pulled out it becomes an absolute value?
Zarkon
  • Zarkon
\[\sqrt{x^6}=|x^3|\]
anonymous
  • anonymous
thanks for going through the trouble @UnkleRhaukus!
anonymous
  • anonymous
and you too Zarkon!
UnkleRhaukus
  • UnkleRhaukus
ah that is what to do if you have a negative index im glad learn something (thanks zarkon and thanks hicksonm

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