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Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$

  1. is $\mid z \mid > \frac{1}{9} \\$
  2. is $\mid z \mid < \frac{1}{3} \\$
  3. is $\frac{1}{3}>\mid z \mid > \frac{1}{9} \\$
  4. does not exist
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