Sequences Quiz

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1. Find the limit of $a_n = \dfrac{n}{\sqrt{9n^2 + 1}}$.

   (a) $\dfrac{1}{3}$
   (b) $\dfrac{1}{9}$
   (c) $\dfrac{1}{\sqrt{3}}$
   (d) $0$

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2. Find the limit of $a_n = 1.2^n$.

   (a) $1$
   (b) $0$
   (c) $\infty$
   (d) $\sqrt{\sqrt{1.2} - 1}$

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3. Find the limit of $a_n = (1 + x/n)^n$.

   (a) $0$
   (b) $x$
   (c) $\infty$
   (d) $e^x$

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4. Find $$\lim_{n \to \infty} 3^{2/n}.$$

   (a) $0$
   (b) $1$
   (c) $3$
   (d) $\infty$

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5. Let $a_n = \dfrac{3 + \sin{\left(n\right)}}{\sqrt{n}}$. Find $\lim_{n \to \infty} a_n$.

   (a) $0$
   (b) $1$
   (c) $3e$
   (d) $\infty$

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