*21. Prove that if |x - xol < min and ly – yol < 2(1yol +1) ' 2(\xol + 1)' then |xy – xoyol < 8. (The notation “min" was defined in Problem 13, but the formula provided by that problem is irrelevant at the moment; the first inequality in the hypothesis just means that |x - xol < and x – xol < 1; 2(\yol +1) at one point in the argument you will need the first inequality, and at an- other point you will need the second. One more word of advice: since the hypotheses only provide information about x – xo and y – yo, it is almost a foregone conclusion that the proof will depend upon writing xy – xoyo in a way that involves x – xo and y – yo.)
*21. Prove that if |x - xol < min and ly – yol < 2(1yol +1) ' 2(\xol + 1)' then |xy – xoyol < 8. (The notation “min" was defined in Problem 13, but the formula provided by that problem is irrelevant at the moment; the first inequality in the hypothesis just means that |x - xol < and x – xol < 1; 2(\yol +1) at one point in the argument you will need the first inequality, and at an- other point you will need the second. One more word of advice: since the hypotheses only provide information about x – xo and y – yo, it is almost a foregone conclusion that the proof will depend upon writing xy – xoyo in a way that involves x – xo and y – yo.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:*21.
Prove that if
|x - xol < min
and ly – yol <
2(1yol +1) '
2(\xol + 1)'
then |xy – xoyol < 8.
(The notation “min" was defined in Problem 13, but the formula provided by
that problem is irrelevant at the moment; the first inequality in the hypothesis
just means that
|x - xol <
and x – xol < 1;
2(\yol +1)
at one point in the argument you will need the first inequality, and at an-
other point you will need the second. One more word of advice: since the
hypotheses only provide information about x – xo and y – yo, it is almost a
foregone conclusion that the proof will depend upon writing xy – xoyo in a
way that involves x – xo and y – yo.)
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