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Math Help - continuity question check

  1. #1
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    continuity question check

    Consider the following graph of a function F

    F(x) =

    1/x --> x < -1
    2 --> -1 (less than or equal to) x < 1
    3 --> x = 1
    x+1 --> 1 < x (less than or equal to) 2
    -1/(x-2) --> 2 < x

    (a) Find lim x-->1- F(X)
    (b) Find lim x-->-1+ F(X)
    (c) Find lim x-->-1 F(X)
    (d) Find lim x-->1 F(X)
    (e) Is F continuous at x=1


    this is what i got for the answers

    (a) 1/x
    (b) 2
    (c) 2
    (d) none
    (e) no


    are these answer correct?
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  2. #2
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    Quote Originally Posted by break View Post
    Consider the following graph of a function F

    F(x) =

    1/x --> x < -1
    2 --> -1 (less than or equal to) x < 1
    3 --> x = 1
    x+1 --> 1 < x (less than or equal to) 2
    -1/(x-2) --> 2 < x

    (a) Find lim x-->1- F(X)
    (b) Find lim x-->-1+ F(X)
    (c) Find lim x-->-1 F(X)
    (d) Find lim x-->1 F(X)
    (e) Is F continuous at x=1


    this is what i got for the answers

    (a) 1/x
    (b) 2
    (c) 2
    (d) none
    (e) no


    are these answer correct?

    No. for (a) you have lim 2 when x --> 1- since F(x) = 2 for -1 x < 1.
    (b) is right. (c) is "doesn't exist", since lim F(x) when x --> -1- doesn't equal lim F(x) = -1+: the former is 1/-1 = -1, whereas the latter is 2.
    Also (d) is incorrect: the limit exists since both one-sided limits equal 2. That none of these equals F(1) only means F(x) isn't continuous at x = 1, but still the limit exists.
    (e) is correct but for the reasons above, not for what you thought.

    Tonio
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  3. #3
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    oops had a typo

    (a) is supposed to be

    (a) Find lim x-->-1- F(X)


    and also is (d) 3?
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  4. #4
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    Quote Originally Posted by break View Post
    oops had a typo

    (a) is supposed to be

    (a) Find lim x-->-1- F(X)


    and also is (d) 3?

    (a) Then even worse: the limit doesn't exist.

    The answer for (d) and its reason I wrote in my past message

    Tonio
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