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

#### Roberto37

##### New member
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

##### Moderator
Staff member
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

##### Elite Member
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

##### New member
Lim (f(x)g(x)) = lim f(x) * lim g(x) if they both exist
I think the letter b is correct , and you?