A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

watchmath

  • 5 years ago

Limit and circle The problem is attached

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

    \(C_1\) is a fixed circle given by \((x-1)^2+y^2=1\) and \(C_2\) is a shriking circle with radius \(r\). \(P\) is the point of \((0,r)\), \(Q\) is the upper point of intersection of the two circles,a nd \(R\) is the point of intersection of the line \(PQ\) and the \(x\)-axis. WHat happens to \(R\) as \(C_2\) shrinks, that is, as \(r\to 0^+\)?

    1 Attachment
  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it moves toward the y axis

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

    if a^3 = b^3 + c^3 + d^3 , then least value of a is ?

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

    PLS HELP

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

    @ishan Do you mean \(\lim_{r\to 0^+}R=0\)? That is not correct!! Try again :D

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

    the Y(op)-->0 and PR-->0R

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

    if a^3 = b^3 + c^3 + d^3 , then least value of a is ?

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

    eventually the shrinking circle will have radius 0 and it will just be a point on the origin and P=Q drawing a line from P to Q would then give a horizontal line on the x axis

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

    P=Q because C1 and C2 intersect at the origin

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

    You need to work out this more rigorously. Your intuition can deceive you here.

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

    the slope of PQR is -r/R (using P=(0,r) and R=(R,0)) so as r goes to zero the slope of PQR are getting closer to zero

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

    But we are interested in finding R (as r-->0 ). How is the fact that you mention helping us?

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

    R is the x-intercept of PQ so i'm not seeing how the line PQ isn't approaching the x-axis or y=0

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

    meaning R would be every point on the x-axis since PQ is that line I don't know its late

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

    i go to sleep and dream about it tonight k?

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

    oops this morning its 3:34 am

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

    well if the slope is approaching 0 and the line isn't moving toward the x-axis, then that would mean the line PQ is getting closer to not having a x-intercept (R) since PQ is a constant not equal to 0

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

    It is 4:42 here :). I think dumbcow will answer this, right? :D

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

    limit as r->0 is 4

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

    not 100% but i was able to get R as a function of r

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

    Yes, then now it is just an exercise of computing limit.

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

    \[R =\frac{r^{2}}{2-\sqrt{4-r^{2}}}\] use L'hopitals rule

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

    first i set the 2 circle equations equal to each other to find Q in terms of r then determined slope with P and Q used equation of a line to find R the x-intercept

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

    thats right Q is the intersection of the two circles :(

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

    btw thanks for the diagram could not have done this without that, im a visual person :)

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

    ok i guess i see how it can be 4 lol

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

    what about what i mention? why is it wrong? i mean i know its wrong because it doesn't give the right answer, but what makes it wrong to do

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

    P=(0,r) R=(R,0) the slope of PQ is r/(-R) this shows as r goes to zero tha PQ is getting closer to being a horizontal line

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

    yes slope is getting flatter which pushes the x-intercept farther out so there is just a limit to how far out it can go so you are not wrong on that point

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

    but it never totally goes flat okay i get it

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

    meaning there is a x-intercept

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

    right P approaches the origin and PQ approaches the x-axis but dont ever get there :)

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

    because we never get to the origin lol

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

    thanks cow

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

    your welcome watchmath did that answer all your questions

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

    watchmath give me another i want to prove i can think like a pro

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

    don't do it now wait til tomorrow let me sleep if you give it to me now then i will never sleep

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

    ok the fixed circle EQ is (x-1)^2 +y^2=1...the other circle is at the center with (h,k)=(0,0) therefore the EQ is x^2 + y^2 =r^2 are you geting it watch?

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

    now in this two EQ, you can compute the intersection PQ and get its X and Y

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

    now once you get the x and y, you can get its hypotenuse which is the PQ..then from there you can set the limit as r-->0

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

    now i dont know if Q is fixed there at that point, or changed position with the other circle, as r--->0

  42. 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.