Limits of a Sequence (Leaving Cert Mathematics): Quizzes

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Limits of a Sequence
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13 questions from this quiz

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What does it mean when a sequence converges?

It has a finite limit

What does it mean when a sequence diverges?

It has infinite limit or no limit

Is the sequence 1,3,5,7,...1, 3, 5, 7, ... convergent or divergent?

Divergent

What is the limit of the sequence 0.3,0.33,0.333,...0.3, 0.33, 0.333, ...?

13\frac{1}{3}

Why is the sequence 2,2,2,2,...2, -2, 2, -2, ... divergent?

The limit does not exist

What is limn5(4n2)\lim_{n \to 5} (4n-2)?

1818

According to the Constant Rule, limxac\lim_{x \to a} c equals what?

cc

What is limxacf(x)\lim_{x \to a} cf(x) by the Constant Multiple Rule?

climxaf(x)c\lim_{x \to a} f(x)

By the Sum Rule, limxa(f(x)+g(x))\lim_{x \to a}(f(x) + g(x)) equals what?

limxaf(x)+limxag(x)\lim_{x \to a}f(x) + \lim_{x \to a}g(x)

What is limx(1x)\lim_{x \to \infty} \left(\frac{1}{x}\right)?

00

What is limxkx\lim_{x \to \infty} k^x when 1<k<1-1 < k < 1?

00

Why must we take extra steps when evaluating limits that approach \frac{\infty}{\infty}?

\frac{\infty}{\infty} is not defined

When evaluating limx3x2x+5\lim_{x \to \infty} \frac{3x}{2x+5}, what should you do first?

Factor out xx from numerator & denominator

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