Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

muffin

  • one year ago

Evaluate the limit, if it exists lim h-0 ((1/(x+h)^2 - 1/x^2 ))/ h

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

    Try combining top fractions. And get rid of the compound fraction. Unless you already know derivatives then we can actually skip this part.

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

    so a common denominator for the top fractions? do i expand the (x+h)^2

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

    You will need to.

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

    so x^2 + 2xh + h^2, what would be the common denominator

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

    x^2(x+h)^2

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

    |dw:1379983226588:dw|

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

    |dw:1379983241382:dw|

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

    2xh + h^2/ x^2 (x+h)^2 x (1/h)

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

    can i factor out a h from the numerator?

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

    so i factored out an h from the numerator, than cancelled the h from 1/h

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

    What happen to your negative in from 2xh?

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

    h/h=1 yep yep

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

    i have lim h--0 2x+h/ x^2(x+h)^2

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

    so now i can "sub" in 0 into h, but what value goes for x?

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

    Well yeah but still you are missing a negative on top

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

    only h is going somewhere x stays

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

    It said what happens as h goes to zero (it said nothing for x)

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

    Did you figure out what negative you are missing?

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

    ok i think i see my mistake so i went thru the stages again and right now I have lim h--0 -2x-h/x^2 (x+h)^2

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

    because I factored out an h, but im confused as to my next step

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

    h goes to 0

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

    is my answer suppose to be just a number? or will it have a value and x

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

    Your answer will be a function of x.

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

    -2x-0/x^2 (x+0) ^2 ?

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

    (-2x-0)/(x^2(x+0)^2) yes Simplify.

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

    -2/x?

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

    not rlly syre how to simplify the denominator

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

    \(\cfrac{(-2x-0)}{(x^2)(x+0)^2}\) (Just for ease - wrote the LaTeX)

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

    -2x-0=-2x x^2(x+0)^2=x^2(x)^2 (since x+0=x) Use law of exponents.

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

    Recall one of the laws of exponents a^m * a^n=a^(m+n)

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

    ok so my answer is -2/x^3

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

    yep

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

    thank you :)

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

    But the denominator should be x^4 @myin

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

    -2x/x^4=-2/x^3

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

    I have another question: find the limit if it exists limx-- -2 2-|x|/ 2+x

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

    thats lim x approaches -2

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

    can I just sub in -2 for x? so that makes it 0/0

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

    Oh sorry @myininaya - didn't saw that :) Thanks !

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

    \[\lim_{x \rightarrow -2} \frac{2-|x|}{2+x}\] ?

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

    yes

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

    So we can't just simply plug in -2 because our denominator will be 0. Is there someway to make the function continuous at x=-2 so we can just plug in Well |x|=x if x>=0 and -x if x<0 Since x approaches -2 then x is negative since we are looking at what surrounds a negative number so we have |x|=-x

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

    That is your key ingredient

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

    okay

  45. 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.