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    Finding a Function that Satisfies a Limit

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    Find a formula for a function f, that satisfies the following conditions:
    1. lim(x->+/-infinity)f(x) = 0,
    2. lim(x->0)f(x) = -infinity,
    3. lim(x->3-)f(x) = infinity,
    4. lim(x->3+)f(x) = -infinity,
    5. f(2) = 0.

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    Solution Summary

    Functions are found that satisfy limits. The solution is detailed and well presented.