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Math Help - Prove that f has a limit at 1

  1. #1
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    Prove that f has a limit at 1

    Ugh more review sheets!

    Define: f0,1) -> R by f(x) = ( x^3- x^2+x-1)/(x-1). Prove that f has a limit at 1.

    It says that we shouldn't have to use epsilon and delta so that blew my whole idea of showing it was < epsilon. So would I got about it by dividing everything by x^3 and so on? or do I need to show an actual proof?

    thanks
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by tn11631 View Post
    Ugh more review sheets!

    Define: f0,1) -> R by f(x) = ( x^3- x^2+x-1)/(x-1). Prove that f has a limit at 1.

    It says that we shouldn't have to use epsilon and delta so that blew my whole idea of showing it was < epsilon. So would I got about it by dividing everything by x^3 and so on? or do I need to show an actual proof?

    thanks

    Factor the numerator

    x^3-x^2+x-1=x^2(x-1)+(x-1)=(x-1)(x^2+1)
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    Factor the numerator

    x^3-x^2+x-1=x^2(x-1)+(x-1)=(x-1)(x^2+1)
    so then I just plug in 1 from the f: (0,1) -> R , which would make the limit zero at 1? and I don't have to worry about 0 from f: (0,1), and I don't have to worry about a fancy proof? lol sorry I just want to make sure
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    Factor the numerator

    x^3-x^2+x-1=x^2(x-1)+(x-1)=(x-1)(x^2+1)
    Duh I had this wrong..lol After we factor it we end up with ( x^2+1) b.c every thing else cancels so then the limit at 1 is 2..lol thanks for the help!
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