A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

hpfan101

  • one year ago

\[\lim_{x \rightarrow 0^-}(\frac{ 1 }{ x }-\frac{ 1 }{ \left| x \right| })\]

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

    When \(x\to0^-\), that means that \(x<0\), so \(|x|=-x\). \[\frac{1}{x}-\frac{1}{|x|}=\frac{1}{x}+\frac{1}{x}=\frac{2}{x}\]

  2. hpfan101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh ok, thank you! So if there's an absolute value and x is less than 0, we just change the sign?

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

    Kind of, it depends on the values of \(x\) you're considering. The absolute value of a number is defined by \[|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x<0\end{cases}\] This means whenever \(x\) is some positive number, its absolute value is the same number, i.e. \(|x|=x\). If \(x\) is a negative number, then the absolute value will cancel that sign to make it positive. But it wouldn't be true that \(|x|=x\) because \(x\) is negative. For example, the previous equation would suggest that \(|-2|=-2\), but that's not true. We make up for the sign by making \(|x|=-x\) whenever \(x\) negative.

  4. hpfan101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh I see. Thanks for the explanation!

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

    yw

  6. 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.