Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Eyad

  • 3 years ago

\huge lim_{x rightarrow 1} frac{sqrt[5]{2x+1}-1}{sqrt[4]{2x+1}-1}

  • This Question is Closed
  1. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\lim_{x \rightarrow 1}\frac{\sqrt[5]{2x+1}-1}{\sqrt[4]{2x+1}-1}\] Correct?

  2. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Is so the function is continuous at x=1 so just plug it right on in :)

  3. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    if not is *

  4. Eyad
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @myininaya : sry i wrote it wrong ,Limit Tends to 0 .

  5. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok and hey which way do you prefer to do this? algebraically or l'hospital?

  6. Eyad
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    algebraically

  7. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\lim_{x \rightarrow 0}\frac{\sqrt[5]{2x+1}-1}{\sqrt[4]{2x+1}-1}\] 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 \[(u^{20})^\frac{1}{4}=(2x+1)^\frac{1}{4} => u^5=\sqrt[4]{2x+1}\]

  8. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So if x goes to 0 then what does u go to ?

  9. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[u^{20}=2x+1 => u=(2x+1)^\frac{1}{20} \text{ correct?}\] So can you tell me what u goes to if x goes to 0?

  10. myininaya
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Eyad we are almost there :)

  11. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy