Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

baldymcgee6 Group Title

Tricky limit?

  • 2 years ago
  • 2 years ago

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

    sorry, thats kind of hard to see.

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

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

    • 2 years ago
  4. wio Group Title
    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: \(x=1/n\) \[\Large e = \lim_{x \rightarrow 0}\left(1+x\right)^\frac{1}{x} \]

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

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

    • 2 years ago
  6. baldymcgee6 Group Title
    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

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

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

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

    right.

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

    |dw:1353045336700:dw|

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

    |dw:1353045499277:dw|

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

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

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

    I can't read that bottom line.

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

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

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

    No, of the previous picture

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

    I don't know

    • 2 years ago
  16. wio Group Title
    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.

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

    |dw:1353047217870:dw|

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

    |dw:1353047297672:dw|

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

    @waterineyes can you help me understand this maybe?

    • 2 years ago
    • Attachments:

See more questions >>>

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.