Question

For irrational x \in R, one can define e^{x} to be lim e^{a_{n}}, where (a_{n}) is any sequence of rational numbers converging to x. Prove that this is well-defined and that E(x)=e^{x}.

Name: for irrational x in r one can define ex to be lim ean where an is any sequence of rational numbers converging to x prove that this is well defined and that exex 00916
Uploaded: 2022-09-27T08:57:40-08:00
Duration: 3 min 33 s
Channel: Adi S
Description: for irrational x in r one can define ex to be lim ean where an is any sequence of rational numbers converging to x prove that this is well defined and that exex 00916

          For irrational x \in R, one can define e^{x} to be lim e^{a_{n}}, where (a_{n}) is any sequence of rational numbers converging to x. Prove that this is well-defined and that E(x)=e^{x}.

Added by Rachael J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/27/2022

Step 1

This means that regardless of the choice of the sequence \( (a_n) \), the limit should yield the same value. Show more…

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For irrational x \in R, one can define e^{x} to be lim e^{a_{n}}, where (a_{n}) is any sequence of rational numbers converging to x. Prove that this is well-defined and that E(x)=e^{x}.