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Math Help - can someone check my work on this relaively easy limit problem

  1. #1
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    can someone check my work on this relaively easy limit problem

    5. Find all the local and absolute extrema (maxima and minima) for
    f
    (x) = x^3 +1 for x<1
    1/x + 1 for x greater than or equal to 1

    also calculate the limits as x goes to + and - infinity



    i got local max when x=1
    i dont think there are any absolute extrema

    and i think the lim as x goes to +infinity is 0
    and as x goes to -ininity is positive infinity...how do i show thats the case?

    am i right on all counts?

    unfortunately ill be on here for the next 2-3 hours or so, so if you could help me with any of the questions ive yet asked id be extremely grateful (with my last and worst one still to come)


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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by twostep08 View Post
    5. Find all the local and absolute extrema (maxima and minima) for



    f
    (x) = x^3 +1 for x<1

    1/x + 1 for x greater than or equal to 1



    also calculate the limits as x goes to + and - infinity





    i got local max when x=1
    i dont think there are any absolute extrema



    and i think the lim as x goes to +infinity is 0
    and as x goes to -ininity is positive infinity...how do i show thats the case?



    am i right on all counts?



    unfortunately ill be on here for the next 2-3 hours or so, so if you could help me with any of the questions ive yet asked id be extremely grateful (with my last and worst one still to come)


    I believe your function is f(x)=\begin{cases} x^3+1 & \mbox{if}\quad x<1 \\ 1+\frac{1}{x} & \mbox{if}\quad x\geqslant 1\end{cases}

    For the limits, clearly \lim_{x\to\infty}f(x)=1, right? Also, \lim_{x\to-\infty}f(x)=-\infty.
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  3. #3
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    right you are...im gettin tired havent slept in a long time. are my mins/maxs right? and how should i show the limit approaches those?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by twostep08 View Post
    right you are...im gettin tired havent slept in a long time. are my mins/maxs right? and how should i show the limit approaches those?
    To be honest, I am not in a min-max mood right now :/. To show them you would have to do \delta-\varepsilon.
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