Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

baldymcgee6

  • 2 years ago

Tricky limit?

  • This Question is Closed
  1. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\lim_{x\to 0}\left(\frac{(1+x)^{\frac{1}{x}}}{e}\right)^{\frac{1}{x}}.\]

  2. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, thats kind of hard to see.

  3. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\LARGE \lim_{x\to 0}\left(\frac{(1+x)^{\frac{1}{x}}}{e}\right)^{\frac{1}{x}}.\]

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

    \[ \Large e = \lim_{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^n \]When you reparameterize: \(x=1/n\) \[\Large e = \lim_{x \rightarrow 0}\left(1+x\right)^\frac{1}{x} \]

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

    So it's a matter of settling that outer 1/x

  6. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I haven't learned 'reparameterize' yet, so I would assume I wouldn't have to use that... Supposed to use L'Hospital's rule

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

    Okay, then you need to have an indeterminate form of \(\infty /\infty\) or \(0/0\)

  8. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right.

  9. mahmit2012
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353045336700:dw|

  10. mahmit2012
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353045499277:dw|

  11. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mahmit2012 I am supposed to use L'Hospital's rule.

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

    I can't read that bottom line.

  13. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    "and in this case it is 1/sqrt(e)

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

    No, of the previous picture

  15. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know

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

    Okay, let's start with bringing in the \(1/x\) to the numerator and denominator and figuring out if that is an indeterminate form.

  17. mahmit2012
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353047217870:dw|

  18. mahmit2012
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353047297672:dw|

  19. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @waterineyes can you help me understand this maybe?

  20. 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

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.