Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

j814wong Group Title

Define f(x) so that ((x^3)-(x^2)-x-2)/((x^2)-4) is continuous at x = 2.

  • one year ago
  • one year ago

  • This Question is Closed
  1. j814wong Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I know what it means for a function to be continuous at a certain point and I know that the above function is not continuous at x = 2. But I don't understand what the question means when it asks for one to define the function.

    • one year ago
  2. zepdrix Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmmm i think they're asking you to do something like this.|dw:1348695324335:dw| we need to find a value for c that will make it a nice smooth curve so whats happening is.. you have a HOLE at x=-2, and at x=2. So we want to go in and patch the hole

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

    |dw:1348695490464:dw|woops i missed one of the points :x

    • one year ago
  4. zepdrix Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so the way to find the y value of the HOLEs is to approach the hole from the left or right :D what operation allows us to get closer and closer and closer to a point, without actually touching it?

    • one year ago
  5. j814wong Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Limits?

    • one year ago
  6. j814wong Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So I'll want to find the left and right limits then?

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

    mm yes i think so :D let me check first, i dont wanna lead you down the wrong path if i made a mistake.

    • one year ago
  8. zepdrix Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm ok this problem is a bit nasty, since you need to factor a term out of a cube. I dont really remember how to do that part, i had to enter it into wolfram :( |dw:1348696335593:dw| lemme rewrite the initial function, cause i think i made a tiny notation error :) so we would have this so far..|dw:1348696501525:dw|

    • one year ago
  9. zepdrix Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so f(x)=7/4 will plug the hole at x=2 now we need to plug the hole at x=-2.. so we'll have to do similar to what we did before, except we need to try and factor an (x+2) from that darn cube D: any of this making sense? XD

    • one year ago
  10. j814wong Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I got most of it except why did you choose to get a c1 and c2? Or rather,how did you know that x is not equal to -2? In this case, is c defined as the value that plugs in the gap?

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

    that's why i corrected the chart, it's not x=c1, its f(x) = c1 , when x=2 the c1 is the Y value that we needed

    • one year ago
  12. j814wong Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Where did you get the x=/= -2 though?

    • one year ago
  13. zepdrix Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1348697608343:dw| lets pretend the graph looks like this see the holes at -2 and 2? those are making our function discontinuous. so to fix that that, we change the function to a piece-wise function and we say "no no no, when x=-2 or 2, we'll define with a different piece than this function"

    • one year ago
  14. j814wong Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh ok then. Thanks a lot.

    • one year ago
    • Attachments:

See more questions >>>

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.