How would one compute lim δ → 0 , k → ∞ ( 1 + δ ) a k , where a is some positive constant?

Question

How would one compute       lim          δ      →      0      ,      k      →      ∞        (  1  +  δ      )          a      k      , where a is some positive constant?

Reese King · Accepted Answer

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

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

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New Questions in Calculus 1