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Math Help - New to Calculus, need help with Limits from Graphs

  1. #1
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    New to Calculus, need help with Limits from Graphs

    I have a math problem I need help with. I tried to do it but I wasn't really sure on any of them, and the last two (d and e) I have no idea how to do.

    Question: Which of the following statements about the function y = f(x) graphed here are true and which are false?

    Picture of the graph in the textbook(I recreated it as best as I could using Microsoft Paint):

    a. lim f(x) does not exist.
    x->2

    My answer for a: False? I wrote "because it does not matter whether or not if the "circle" is shaded in". There is a line going over the part at 2, so I guess it does exist as x-> 2?

    b. lim f(x) = 2
    x->2

    My answer for b: true?

    c. lim f(x) does not exist
    x->1

    My answer for c: false? The dot is there at 1 so it's false?

    d. lim f(x) exists at every point x0 in (-1, 1).
    x->x0(x over 0)

    My answer for d: I don't understand the question or how to do this

    e. lim f(x) exists at every point x0 in (1, 3).
    x-> x0(x over 0)

    My answer for e: Same as d, don't know.

    Any help will be appreciated it, thanks in advance.
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  2. #2
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    For part b the statement is false, because the graph is defiantly not near y=2.

    Part a the limit may be 1, but I'm not sure as it's been a long time since I've done any of these questions. I say this because as x approaches 1 from the left and right, the function appears to go to 1.

    I don't understand questions d and e either, what do you mean by the "(over zero)" thing?
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  3. #3
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    Thanks for the reply. For d and e, here are the questions for d and e again, they look kind of like this in the text book.

    d. lim f(x) exists at every point x0 in (-1, 1).

    My answer for d: I don't understand the question or how to do this

    e. lim f(x) exists at every point x0 in (1, 3).

    My answer for e: Same as d, don't know.
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  4. #4
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    I've never heard a question asked this way but what I think it's asking is that "is x continuous as it approaches any of the numbers from 1 to 3" (or whatever the range).

    So for d and e no x's isn't continuos because for (-1,1) there is a kink at x=0 and for (1,3) there is a jump discontinuity at 2
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