A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Limit Problem-to find the value of a and b. Can anyone help me to do the problem? http://i.imgur.com/rp4ifCl.png

  • This Question is Open
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It looks nasty. My suggestion would be to use l'Hospital's rule in a "reverse" manner. See the way we usually use it is in a forward manner - we evaluate the limit of the numerator and the denominator, and then we apply l'Hospital's rule to find the limit (if it exists). Here we know the limit exists, and we know that both the numerator and the denominator tend to 0. Suppose the numberator was f(x) and denominator was g(x) then: lim of f(x)/g(x) as x->0 = lim of f'(x) / g'(x) as x->0 = 1

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

    Please someone help.

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see no theoretical reason why it shouldn't work. We press on then to find f'(x) and g'(x). f'(x)=3*x^2 g'(x)=*oh gods*[ 1/( 2*sqrt(a+x) )] * [bx-sin(x)] + sqrt(a+x) *[b-cos(x)]

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

    It's a pain in the retricemethod but once you get f'''(x) and g'''(x), the idea is that f'''(x)=1 and you will say that g'''(x) will also have to equal 1 for the limit itself to equal 1 and that should give you some information about a and b. Again, it's a pelletty method but I see no way around this.

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But it is becoming very lengthy

  6. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you know about power series?

  7. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll show you the method:

  8. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Large\sf{\color{blueviolet}{\lim_{x\rightarrow0}\frac{x^3}{\sqrt{a+x}(bx-sinx)}\\=\lim_{x\rightarrow0}\frac{x^3}{\sqrt{a+x}\left(bx-\left(\frac{x}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}\ldots\right)\right)}}}\]

  9. amilapsn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now it's a matter of guessing what a and b should be for the limit to be 1. I leave you to ponder over it....

  10. 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.