Consider the function g(x) = (1 + 1/x) x + a . Show that if 0

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Consider the function g(x) = (1 + 1/x)^{x + a}. Show that if 0 ≤ a < 12 , then g(x) → e from below as x → ∞; if 1/2 ≤ a < 1, then g(x) → e from above as x →∞.

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First observe that Therefore It suffices to determine whether ln gx 1 is positive or negative ...View the full answer

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