Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

aiskarl

  • 2 years ago

give an example

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

    give an example to show that \[\lim_{x \rightarrow a} f(x)\] and \[\lim_{x \rightarrow a} g(x)\] doesnot exist but \[\lim_{x \rightarrow a} (f(x)+g(x))\] exist

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

    try this \[ \lim_{x \to 0}{\sin^2x x \over x^2}\] expand sin^2 x as 1 + cos^2x

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

    let f(x)=x and g(x)=-(x+1) and a=infinity then \[\lim_{x \rightarrow \infty } f(x)=\infty \] and \[ \lim_{x \rightarrow \infty } g(x)=-\infty\] but \[ \lim_{x \rightarrow \infty}f(x)+g(x)=-1\]

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

    try something like of this form where you can take LCM and use L'Hopital's rule \[ \infty - \infty \]

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

    @REMAINDER 's example is also good example.

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

    Woops!! \[ \lim_{x \to 0}{\sin^2x \over x^2} = \lim_{x \to 0}{1 \over x^2}+\lim_{x \to 0}{\cos^2 x \over x^2}\]

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

    ???

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

    both 1/x^2 and cos^2x/x^2 does not exist but the sum exists

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

    how to know exist or not

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

    try finding them individually ...

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

    http://www.wolframalpha.com/input/?i=lim+x-%3E0+cos^2x%2Fx^2

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.