anonymous
  • anonymous
\huge lim_{x rightarrow 1} frac{sqrt[5]{2x+1}-1}{sqrt[4]{2x+1}-1}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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myininaya
  • myininaya
\[\lim_{x \rightarrow 1}\frac{\sqrt[5]{2x+1}-1}{\sqrt[4]{2x+1}-1}\] Correct?
myininaya
  • myininaya
Is so the function is continuous at x=1 so just plug it right on in :)
myininaya
  • myininaya
if not is *

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anonymous
  • anonymous
@myininaya : sry i wrote it wrong ,Limit Tends to 0 .
myininaya
  • myininaya
Ok and hey which way do you prefer to do this? algebraically or l'hospital?
anonymous
  • anonymous
algebraically
myininaya
  • myininaya
\[\lim_{x \rightarrow 0}\frac{\sqrt[5]{2x+1}-1}{\sqrt[4]{2x+1}-1}\] Let me think on the algebraic approach I think it might be a substitution So the lcm of 5 and 4 is 20 So lets try the sub \[u^{20}=2x+1\] So that means \[(u^{20})^\frac{1}{5}=(2x+1)^\frac{1}{5} => u^4=\sqrt[5]{2x+1}\] and \[(u^{20})^\frac{1}{4}=(2x+1)^\frac{1}{4} => u^5=\sqrt[4]{2x+1}\]
myininaya
  • myininaya
So if x goes to 0 then what does u go to ?
myininaya
  • myininaya
\[u^{20}=2x+1 => u=(2x+1)^\frac{1}{20} \text{ correct?}\] So can you tell me what u goes to if x goes to 0?
myininaya
  • myininaya
Eyad we are almost there :)

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