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June 3rd, 2018, 05:29 PM   #1
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Math analysis

Can someone please help? Iam Brazil
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June 3rd, 2018, 06:11 PM   #2
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What do you think about the first one? Just give us your thoughts, don't even edit yourself. Just think about the problem, what it's asking, why it might or might not be true.

Is your language Portuguese? I speak a little Spanish. To me, Portuguese is sort of like Spanish and nothing at all like Spanish at the same time. It's like I "should" be able to understand it but a lot of times I can't.
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Last edited by Maschke; June 3rd, 2018 at 06:25 PM.
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June 4th, 2018, 02:49 PM   #3
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I tried to translate in Google, do you understand?
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Last edited by skipjack; June 5th, 2018 at 06:34 AM.
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June 4th, 2018, 03:23 PM   #4
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Quote:
Originally Posted by Roberto 37 View Post

I tried to translate in Google, do you understand?
What do you think about the first one? Just give us your thoughts, don't even edit yourself. Just think about the problem, what it's asking, why it might or might not be true.

Last edited by skipjack; June 5th, 2018 at 06:35 AM.
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June 4th, 2018, 05:15 PM   #5
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I think the letter c is correct; options I and II true.

Last edited by skipjack; June 5th, 2018 at 06:35 AM.
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June 4th, 2018, 08:52 PM   #6
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July 12th, 2018, 08:19 AM   #7
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In general, as long as two sequences, $\displaystyle \{an\}$, $\displaystyle \{bn\}$, have finite sums, it is true that
$\displaystyle \lim_{n\to\infty} (a_n+ b_n)= \lim_{n\to\infty} a_n+ \lim_{n\to\infty} b_n$.

$\displaystyle \lim_{n\to\infty} (a_n- b_n)= \lim_{n\to\infty} a_n- \lim_{n\to\infty} b_n$

$\displaystyle \lim_{n\to\infty} (a_n)(b_n)= (\lim_{n\to\infty} a_n)(\lim_{n\to\infty} b_n)$.

$\displaystyle \lim_{n\to\infty}\frac{a_n}{b_n}= \frac{\lim_{n\to\infty} a_n}{\lim_{n\to\infty}}$
(As long as $\displaystyle \lim_{n\to\infty}$ is not 0.)

From that, it follows immediately that options I and II are true. As for III, I have no idea where "2" might have come from! The limit of $\displaystyle \frac{a_n}{a_n}$ is 1, not 0.
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