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Math Help - Left and right hand limits of a hybrid function.

  1. #1
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    Left and right hand limits of a hybrid function.

    Hi, I need help on this one problem: ( I can't type in the format the problem is given, so hopefully it'll be understandable.)
    The question states:

    Evaluate or determine that the limit does not exist for each of the limits (a) lim x--> d- f(x), (b) lim x-->d+ f(x)

    f(x)={ 1/(x+1), for x>-1
    x^2-3x, for x<=(less than and equal) -1

    d=-1


    I think the answer for (a) is 4, and (b) is 4 also, but there are no answer choices (this is multiple choice) for that. The closest is (a) 4, (b) does not exist. I don't understand why (b) is does not exist.

    The answer choices are:

    1) (a) does not exist
    (b) 4

    and

    2) (a) 4
    (b)Does not exist.


    Any help would be appreciated, thanks!
    Last edited by mugenkb2; July 3rd 2011 at 12:18 AM.
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  2. #2
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    Re: Need help limit problem

    Quote Originally Posted by mugenkb2 View Post
    Hi, I need help on this one problem: ( I can't type in the format the problem is given, so hopefully it'll be understandable.)
    The question states:

    Evaluate or determine that the limit does not exist for each of the limits (a) lim x--> d- f(x), (b) lim x-->d+ f(x)

    f(x)={ 1/(x+1), for x>-1
    x^2-3x, for x<=(less than and equal) -1


    Any help would be appreciated, thanks!
    I suppose the value of d is -1 ....?
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Need help limit problem

    Quote Originally Posted by mugenkb2 View Post
    Hi, I need help on this one problem: ( I can't type in the format the problem is given, so hopefully it'll be understandable.)
    The question states:

    Evaluate or determine that the limit does not exist for each of the limits (a) lim x--> d- f(x), (b) lim x-->d+ f(x)

    f(x)={ 1/(x+1), for x>-1
    x^2-3x, for x<=(less than and equal) -1


    Any help would be appreciated, thanks!
    Are you familiar with the definition of limit?
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    Re: Need help limit problem

    Quote Originally Posted by mr fantastic View Post
    I suppose the value of d is -1 ....?
    oh right, I forgot about that, yes, d=-1.


    I think the answer for (a) is 4, and (b) is 4 also, but there are no answer choices (this is multiple choice) for that. The closest is (a) 4, (b) does not exist. I don't understand why (b) is does not exist.

    The answer choices are (should have put them up in the first post) are:

    1) (a) does not exist
    (b) 4

    and

    2) (a) 4
    (b)Does not exist.
    Last edited by mugenkb2; July 3rd 2011 at 12:09 AM.
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  5. #5
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    Re: Need help limit problem

    Quote Originally Posted by mugenkb2 View Post
    oh right, I forgot about that, yes, d=-1.


    I think the answer for (a) is 4, and (b) is 4 also, but there are no answer choices (this is multiple choice) for that. The closest is (a) 4, (b) does not exist. I don't understand why (b) is does not exist.

    The answer choices are (should have put them up in the first post) are:

    1) (a) does not exist
    (b) 4

    and

    2) (a) 4
    (b)Does not exist.
    Option 2) is correct.

    If x --> -1+ then x > -1. Look at the rule for x > -1 and consider what happens in the limit.
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