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4.2.7. Example. If (xn) is a sequence in (0, ∞) and xn → a, then √xn...

4.2.7. Example. If (xn) is a sequence in (0, ∞) and xn → a, then √xn → √a.
?
Proof. Problem. Hint. There are two possibilities: treat the cases a = 0 and a > 0 sepa- √√
rately. For the first use problem 4.1.7(a). For the second use 4.2.1(b) and 4.1.11; write xn − a as |xn − a|/(√xn + √a). Then find an inequality that allows you to use the sandwich theo- rem(proposition 4.2.5).
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Here is the required proof.I hope the solution will help you.Expecting a thumbs up if you are satisfied with the work,it will help me a lot.Thank you.

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