A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

Find the limit:

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

    \[(\int\limits_{0}^{x}(3t-1)^{10} dt)/3x\]

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

    as x approaches 0 I'm confused because the question has two variables: x and t. How should I approach this?

  3. watchmath
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    0

  4. Mr.Math
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Evaluate the limit in the top first.

  5. watchmath
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry, I didn't see 3x :)

  6. watchmath
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Use L'Hospital rule

  7. Mr.Math
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh right. L'Hopital's rule is the best choice: \[\frac{d}{dx}\int\limits_0^x(3t-1)^{10}dt=(3x-1)^{10}.\]

  8. Mr.Math
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The derivative of the bottom is obviously 3. Hence the limit is \(\frac{3(0)-1)^{10}}{3}=\frac{1}{3}\).

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

    This makes sense, but how did you know to use l'hopital's rule?

  10. Mr.Math
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If we plug x=0, you will get \(\frac{0}{0}\). If you plug x in the top, you get an integral from 0 to 0, which results in a value of 0. I think it's very obvious in the denominator.

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

    oh okay, thanks a ton!

  12. 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.