Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    21
    f(x)=x^2 when -1\le x<0
    1 when x=0
    x^2 when 0<x<1
    when 1\le x \le 2




    So \lim_{x\to\0}f(x)=0

    True or False?

    Apparently the answer's true. But I can't understand why. Surely f(x)=1 when x=0? :hmmmm:
    Offline

    1
    ReputationRep:
    (Original post by RamocitoMorales)
    f(x)=x^2 when -1\le x<0
    1 when x=0
    x^2 when 0<x<1
    when 1\le x \le 2
    What conditions must a limit satisfy to exist?
    • Thread Starter
    Offline

    21
    (Original post by Clarity Incognito)
    What conditions must a limit satisfy to exist?
    :dontknow:

    But I'm guessing that it can't be 1 since it is 'static' at that point, i.e x=0, as opposed to being an interval...I think?
    Offline

    1
    ReputationRep:
    (Original post by RamocitoMorales)
    :dontknow:

    But I'm guessing that it can't be 1 since it is 'static' at that point, i.e x=0, as opposed to being an interval...I think?
    It could have been undefined at x=0 but what's important about limits is that we're looking at what happens to f(x) as x tends to 0 from the positive side and the negative side. What happens exactly at the point x=0 is not so important. You can see the left side limit (coming from the negative side of 0) that it approaches 0 and similarly for the right side limit. For a limit to exist, it must have a left side limit and a right side limit and both must approach the same limit.

    My question was ambiguous because it seemed to imply what exactly it means for something to be convergent to a limit but I assume that as you just want to compute these limits that you haven't got to that stage just yet.
    Offline

    11
    ReputationRep:
    (Original post by RamocitoMorales)
    :dontknow:

    But I'm guessing that it can't be 1 since it is 'static' at that point, i.e x=0, as opposed to being an interval...I think?
    It seems that you're trying to justify the continuity of the function rather than the existence of the limit.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.