d
(d) $\mathop {\lim }\limits_{h \to 0} \,\frac{{2\,\left[ {\sqrt 3 \sin \,\left( {\frac{\pi }{6} + h} \right) - \cos \,\left( {\frac{\pi }{6} + h} \right)} \right]}}{{\sqrt 3 \,h\,(\sqrt 3 \,\cos \,h - \sin \,h)}}$
$ = \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}$.