$ = \mathop {\lim }\limits_{h \to 0} \,\frac{{\frac{4}{{\sqrt 3 }}\,\left[ {\frac{{\sqrt 3 }}{2}\sin \,\left( {\frac{\pi }{6} + h} \right) - \frac{1}{2}\cos \,\left( {\frac{\pi }{6} + h} \right)} \right]}}{{h\,(\sqrt 3 \cos \,h - \sin \,h)}}$
$ = \mathop {\lim }\limits_{h \to 0} \frac{4}{{\sqrt 3 }}.\frac{{\sin \,h}}{h}.\frac{1}{{(\sqrt 3 \,\cos \,h - \sin \,h)}} = \frac{4}{3}$.
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$\overrightarrow{ a }=\hat{ i }+\hat{ j }+ n \hat{ k }, \quad \overrightarrow{ b }=2 \hat{ i }+4 \hat{ j }- n \hat{ k } \quad$ and $\overrightarrow{ c }=\hat{ i }+ n \hat{ j }+3 \hat{ k } \quad( n \geq 0),$ is $158 cu. Units$, then
$R =\left\{( x , y ): 5 x ^{2} \leq y \leq 2 x ^{2}+9\right\}$ is ........ $square\, units$