How would one compute lim_(delta => 0, k => infty)(1+delta)^(ak), where a is some positive constant?

Graham Beasley 2022-07-17 Answered
How would one compute lim δ 0 , k ( 1 + δ ) a k , where a is some positive constant?
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Answers (1)

Reese King
Answered 2022-07-18 Author has 13 answers
It’s undefined, because the limit depends entirely on how k and δ 0. For example:
lim k lim δ 0 ( 1 + δ ) a k = lim k 1 a k = 1
lim δ 0 + lim k ( 1 + δ ) a k = lim δ 0 + =
lim δ 0 lim k ( 1 + δ ) a k = lim δ 0 0 = 0
lim δ 0 + ( 1 + δ ) a / δ = lim k ( 1 + 1 b k ) a k = e a / b

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