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A right cone is inscribed in a sphere of radius \( R \). Let \( S=f(x) \) be the functional relationship between the lateral surface area \( S \) of the cone and its generatrix \( x \).
If \( x \) is such that \( x^{n}, n \geq 6 \) is negligible then \( S \) is given by
(a) \( \frac{\pi x^{2}}{2 R}\left(1-\frac{x^{2}}{R^{2}}\right) \)
(b) \( \frac{\pi x^{4}}{2 R} \)
(c) \( \pi x^{2}\left(1-\frac{x^{2}}{8 R^{2}}\right) \)
(d) \( \frac{\pi x^{2}}{2 R}\left(1-\frac{x^{2}}{8 R^{2}}\right) \)
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