Problem 4. number, using the following steps. In(x) xxx0.01 (a) Compute lim (b) Compute lim In(x) 100 -xx+x In x " xxxm We want to obtain the limit lim where m is a positive In(x) In(x) (c) Do you think the result would change for lim lim or lim x→∞ X xx x0.00001 xxx100000 (d) What do your answers to (a) through (c) hint about the relative rates of growth of In(x) In x In(x) o? and xm, m > 0, as x grows very large? Explain in words, and deduce the value lim for m > 0. xxxm

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