Answer
$$1$$
Work Step by Step
$\lim\limits_{x \to \infty} a_n=\lim\limits_{x \to \infty} x^{1/x}\\=\lim\limits_{x \to \infty} e^{1/x \ln (x)}\\=e^{\lim\limits_{x \to \infty} [\dfrac{1}{x} \ln (x)]}\\=e^0\\=1$
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 8 - Sequences and Infinite Series - Review Exercises - Page 658: 5
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