Multiply limits: Given lim[n->infy]x_n = 0, [x_n y_n] = 0, which stmt is correct?

Roberto37

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What we need to observe when we multiply limits?

Sendo \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, x_n\, =\, 0,\) para que

. . .\(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, \left[x_n\, \cdot\, y_n\right]\, =\, 0,\) basta que

. . . . .I) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja negativo

. . . . .II) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja positivo

. . . . .III) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja infinito

. . . . .IV) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja um numero real

a) Only the affirmative I is correct.

b) Only affirmative IV is correct.

c) Only affirmative II is correct.

d) Only affirmative III is correct.



Thank you.
 

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tkhunny

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What we need to observe when we multiply limits?

Sendo \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, x_n\, =\, 0,\) para que

. . .\(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, \left[x_n\, \cdot\, y_n\right]\, =\, 0,\) basta que

. . . . .I) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja negativo

. . . . .II) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja positivo

. . . . .III) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja infinito

. . . . .IV) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja um numero real

a) Only the affirmative I is correct.

b) Only affirmative IV is correct.

c) Only affirmative II is correct.

d) Only affirmative III is correct.



Thank you.
"multiply limits" doesn't mean anything.

If the limit exists, it has a value. Multiply the values.
 
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Jomo

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Dec 30, 2014
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What we need to observe when we multiply limits?

Sendo \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, x_n\, =\, 0,\) para que

. . .\(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, \left[x_n\, \cdot\, y_n\right]\, =\, 0,\) basta que

. . . . .I) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja negativo

. . . . .II) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja positivo

. . . . .III) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja infinito

. . . . .IV) \(\displaystyle \displaystyle \lim_{n \rightarrow +\infty}\, y_n\) seja um numero real

a) Only the affirmative I is correct.

b) Only affirmative IV is correct.

c) Only affirmative II is correct.

d) Only affirmative III is correct.



Thank you.
Lim (f(x)g(x)) = lim f(x) * lim g(x) if they both exist
 
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Roberto37

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