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If \( f(x)=\left\{\begin{array}{cc}\frac{36^{x}-9^{x}-4^{x}+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\ k, & x=0\end{array}\right. \) is continuous at \( x=0 \), then \( k \) equals
(a) \( 16 \sqrt{2} \log 2 \log 3 \)
(b) \( 16 \sqrt{2} \ln 6 \)
(c) \( 16 \sqrt{2} \ln 2 \ln 3 \)
(d) none of these
\( \mathrm{P} \)
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