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    Theorem: Suppose that

    lim as z-->z0 of f(z)=w0 and
    lim as z-->z0 of F(z)=W0

    then

    lim as z-->z0 of [f(z)+F(z)]=w0 + W0,
    lim as z-->z0 of [f(z)F(z)]=w0*W0 and

    if W0 can not equal 0, then

    lim as z-->z0 of f(z)/F(z)=w0/W0.

    Find lim as z--> i of ((iz^3)-1) / (z+i).

    © BrainMass Inc. brainmass.com March 4, 2021, 10:33 pm ad1c9bdddf
    https://brainmass.com/math/functional-analysis/find-the-limit-using-the-given-theorem-341060

    Solution Preview

    Well, if you take
    f(z) = iz^3 - 1
    F(z) = z + i

    then lim (iz^3 - 1)/(z+i) as z goes to i is lim f(z)/F(z).
    Now, if we can find the limits as z->i ...

    Solution Summary

    The theorem is utilized.

    $2.49

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