\textbf{116.} Suppose $a$ is known and $a + n$ is given. Find the value of $\displaystyle\lim_{x \to 0^+} \frac{\tan^2\!\left(\dfrac{1}{\sqrt{1-x^2}}-1\right)}{\left(1-\cos(\sqrt{7x})\right)^n} = a$. What is $a+n$?
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(1) $\dfrac{7}{4}$ \hfill (2) $\dfrac{9}{4}$ \hfill (3) $\dfrac{15}{4}$ \hfill (4) $\dfrac{17}{4}$
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