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Math Help - Limits

  1. #1
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    Limits

    Hey guys I have a few questions I can't do on limits. They are

    i) Consider the functions f(-1,Pie) implies R whose graph y=f(x) is given by - here there's a graph which says y=sin(x) and y=x-x^3 just one line though.

    Prove that the lim f(x)/x as x implies 0 exists.

    I know how to do limits for normal functions like if it was Cos(x) it would tend to 1 and x tended to 0 but don't know how to do this.

    ii) State the definition of Inf(A) and Lim(A) and prove that if lim f(x)=L as x tends to 0 and lim g(x) = M as x tends to 0 then lim(f(x)+g(x))=L+M.

    Don't even know how to start this part to be honest.
    Last edited by Plato; March 3rd 2010 at 12:00 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Mathsnewbie View Post
    Hey guys I have a few questions I can't do on limits. They are

    i) Consider the functions f(-1,Pie) implies R whose graph y=f(x) is given by - here there's a graph which says y=sin(x) and y=x-x^3 just one line though.

    Prove that the lim f(x)/x as x implies 0 exists.

    I know how to do limits for normal functions like if it was Cos(x) it would tend to 1 and x tended to 0 but don't know how to do this.

    ii) State the definition of Inf(A) and Lim(A) and prove that if lim f(x)=L as x tends to 0 and lim g(x) = M as x tends to 0 then lim(f(x)+g(x))=L+M.

    Don't even know how to start this part to be honest.
    I have no idea what this says.
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  3. #3
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    What part or all of it?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Mathsnewbie View Post
    What part or all of it?
    The vast majority of it.
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  5. #5
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    Quote Originally Posted by Mathsnewbie View Post
    Hey guys I have a few questions I can't do on limits. They are

    i) Consider the functions f(-1,Pie) implies R whose graph y=f(x) is given by - here there's a graph which says y=sin(x) and y=x-x^3 just one line though.

    Prove that the lim f(x)/x as x implies 0 exists.

    I know how to do limits for normal functions like if it was Cos(x) it would tend to 1 and x tended to 0 but don't know how to do this.

    ii) State the definition of Inf(A) and Lim(A) and prove that if lim f(x)=L as x tends to 0 and lim g(x) = M as x tends to 0 then lim(f(x)+g(x))=L+M.

    Don't even know how to start this part to be honest.
    Have you read what you wrote?
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