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Math Help - What functions fit these requirements..?

  1. #1
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    What functions fit these requirements..?

    1) lim f(x) =2 where x->3 and f(3) exists

    2) lim f(x) =2 where x->3 but f(3) does not exist

    3) lim f(x) =2 where x->3 and is infinite (does not exist)

    4) lim f(x) =2 where x->3- but lim f(x) where x->3+ does not exist
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  2. #2
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    Quote Originally Posted by yess View Post
    1) lim f(x) =2 where x->3 and f(3) exists

    2) lim f(x) =2 where x->3 but f(3) does not exist

    3) lim f(x) =2 where x->3 and is infinite (does not exist)

    4) lim f(x) =2 where x->3- but lim f(x) where x->3+ does not exist
    I recommend thinking graphically. I also recommend showing some work and saying where you got stuck.
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    Quote Originally Posted by undefined View Post
    I recommend thinking graphically. I also recommend showing some work and saying where you got stuck.
    the problem is i have noooo idea where to start!!
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  4. #4
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    Quote Originally Posted by yess View Post
    the problem is i have noooo idea where to start!!
    Here's another idea then. Think of some common functions like f(x)=x. Does this function satisfy (1)? How about (2)?
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  5. #5
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    for 1) i have f(x) = 3x + 3
    is that ok??
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  6. #6
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    Quote Originally Posted by yess View Post
    for 1) i have f(x) = 3x + 3
    is that ok??
    Why would you think \displaystyle \lim_{x\to3}(3x+3)=2? It's way off.

    Hint: For (1) just choose any function that is continuous everywhere and that satisfies f(3)=2.

    (Note: What I wrote at first wasn't quite right, I edited it.)
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  7. #7
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    Quote Originally Posted by undefined View Post
    Why would you think \displaystyle \lim_{x\to3}(3x+3)=2? It's way off.

    Hint: For (1) just choose any function that is defined everywhere and where f(3)=2.
    ooooh it makes more sense looking at it like that!
    soo maybe x-1 ??
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  8. #8
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    Quote Originally Posted by yess View Post
    ooooh it makes more sense looking at it like that!
    soo maybe x-1 ??
    Yep that works.
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  9. #9
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    so i've got all but 2) .. any hints??
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  10. #10
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    Quote Originally Posted by yess View Post
    so i've got all but 2) .. any hints??
    Draw the graph for f(x)=x-1 except that where x=3 draw a hollow circle..
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