Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ChrisV

  • 3 years ago

lim x>0- ((x+deltaX)^2+x+deltaX-(x^2+x))/deltaX

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

    \[\lim_{x \rightarrow 0-} ((x+\Delta x)^2 +x + \Delta x-(x^2+x)/\Delta x\]

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

    \[\lim_{x \rightarrow 0-} \frac {(x+\Delta x)^2 +x + \Delta x-(x^2+x)}{\Delta x}\]Your gonna have to simplify that out, although it gets annoying...

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

    \[\lim_{\Delta x \rightarrow 0} \frac {(x+\Delta x)^2 +x + \Delta x-(x^2+x)}{\Delta x} = \lim_{\Delta x \rightarrow 0} \frac { x^2 + 2x \Delta x + \Delta^2 x + x - x^2 - x}{\Delta x}\]

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

    yea i did that my problem is after that

  5. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i cancel out the x^2 and X

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

    \[\lim_{\Delta x \rightarrow 0} \frac { x^2 + 2x \Delta x + \Delta^2 x + x + \Delta x - x^2 - x}{\Delta x} = \lim_{\Delta x \rightarrow 0} \frac { 2x \Delta x + \Delta x + \Delta^2 x}{\Delta x} = \lim_{\Delta x \rightarrow 0} 2x + 1 + \Delta x\]

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

    2xdeltax+deltax^2+deltaX/deltax

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

    \[\lim_{\Delta x \rightarrow 0} 2x + 1 + \Delta x = 2x + 1 + 0 = 2x + 1\]

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

    Yeah, divide the delta x's out to simplifiy. Then just evaluate the limit by plugging in 0 for delta x.

  10. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so i factor the deltax out

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

    deltax(2x+deltax+1)/1

  12. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oops i mean over delta x not 1

  13. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so i end up with 2x+deltax+1

  14. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    set delta x to 0

  15. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    gives me 2x+1

  16. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    however the book gives me an answer of -1/x^2

  17. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so im doing something wrong

  18. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so im confused beyond belief atm

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

    -1/x^2 is the answer to another question, probably the derivative of 1/x. The answer to the question you posted here is 2x + 1. There might be an error in the book, or you read it wrong.

  20. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the instruction is to find the limit if it exist, if it does not explain why

  21. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so how do they get a limit of 1/x^2 out of 2x+1?

  22. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well the book does not show me the work in the back, just the answer

  23. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    guess this is one to ask the instructor :)

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

    No, for your question, 2x + 1 is the correct answer. That's all there is to it. You used the limit formula to find the derivative of x^2 + x.\[\frac {dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac {f(x + \Delta x) - f(x)}{\Delta x}\] If you used the same formula for the function 1/x, you would get -1/x^2. You are correct, the textbook is wrong. Don't worry too much about it.

  25. ChrisV
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    k thanks

  26. 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.