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Let \( \mathrm{P}(\mathrm{x}) \) be a polynomial of degree 6 with leading coefficient unity and \( \mathrm{p}(-\mathrm{x})=\mathrm{p}(\mathrm{x}) \forall \mathrm{x} \in \mathrm{R} \).
Also \( (\mathrm{P}(1)+3)^{2}+\mathrm{P}^{2}(2)+(\mathrm{P}(3)-5)^{2}=0 \)
(i) Find the value of \( \operatorname{Lim}_{x \rightarrow-2} \frac{\sin (P(x))}{(x-2) \tan (x+2)} \).
(ii) Find the value of \( \operatorname{Lim}_{x \rightarrow \infty} \frac{\left(x^{2}-\sqrt{\frac{P(x)}{x^{2}-4}}\right)}{x \tan \frac{1}{x}} \).
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