Let a > 0 and recall that (x) = ax-1 and (log x)' = 1/x for all
Question:
a) Prove that log x < xa for x large. Prove that there exists a constant Ca such that log x < Caxa for all x ∈ [1, ∞), Ca → ∞ as α → 0+, and Ca → 0 as a → ∞.
b) Obtain an analogue of part a) valid for ex and xa in place of log x and xα.
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a Let fx log x x Since fx 0 as x fx 1 for large x Also ...View the full answer
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