anonymous
  • anonymous
hey guys i need help solving this limit problem, i know the answer is .25 but i dont know how to show that algebraically i will upload the equation
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
oh and i cant use hospitals rule
Zarkon
  • Zarkon
multiply top and bottom by \[\sqrt{4+x^5}+2\]

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anonymous
  • anonymous
are you sure it is +x^5?
Zarkon
  • Zarkon
yes
Zarkon
  • Zarkon
the only sign change you need in the one in front of the 2
Zarkon
  • Zarkon
from - to +
anonymous
  • anonymous
well that leaves me with 0/0 which is indeterminate form which is bad
Zarkon
  • Zarkon
\[(\sqrt{4+x^5}-2)(\sqrt{4+x^5}+2)=4+x^5-4=x^5\] then cancel the \(x^5\) that is in the numerator and the denominator
Zarkon
  • Zarkon
then take limit
Zarkon
  • Zarkon
\[\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\] \[\lim_{x\to 0}\frac{\sqrt{4+x^5}-2}{x^5}\frac{\sqrt{4+x^5}+2}{\sqrt{4+x^5}+2}\] \[\lim_{x\to 0}\frac{x^5}{x^5(\sqrt{4+x^5}+2)}\] \[\lim_{x\to 0}\frac{1}{\sqrt{4+x^5}+2}\] \[\lim_{x\to 0}\frac{1}{\sqrt{4}+2}=\frac{1}{4}\]
anonymous
  • anonymous
oh ok makes i see now thanks

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