(g) For each fixed k, and each a such that 0 < a < 1, the series Enka" converges and thus, lim na" = 0 (h) Suppose that fn(z)| ≤ M₁ for ne N where (M) is a sequence of positive numbers. Then, the series Ef. (r) con- verges uniformly when M,, converges.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Modified true or false. If it is false, give a counterexample and briefly explain. If true, give a short proof.

(g) For each fixed k, and each a such that
0 < a < 1, the series Enka" converges
and thus, lim na"=0
(h) Suppose that fn(2)| ≤ Mn for ne N
where (M) is a sequence of positive
numbers. Then, the series Ef. (r) con-
verges uniformly when M,, converges.
Transcribed Image Text:(g) For each fixed k, and each a such that 0 < a < 1, the series Enka" converges and thus, lim na"=0 (h) Suppose that fn(2)| ≤ Mn for ne N where (M) is a sequence of positive numbers. Then, the series Ef. (r) con- verges uniformly when M,, converges.
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