The limit $\lim \left[ \left\{ 1 - \cos \left( \sin ^ { 2 } a x \right) \right\} / x \right]$ as $x -> 0$ (a) Equals 1 (b) Equals a (c) Equals 0 (d) Does not exist
(C) Now, $\lim \left[ \left\{ 1 - \cos \left( \sin ^ { 2 } a x \right) \right\} / x \right]$ as $x -> 0$ $= \lim \left[ \left\{ \sin \left( \sin ^ { 2 } a x \right) \times 2 \sin ( a x ) \cos ( a x ) \times a \right\} / 1 \right]$ as $x -> 0$ (Applying L'Hospital) $= \sin \left( \sin ^ { 2 } 0 \right) 2 \sin ( 0 ) \cos ( 0 ) \times a / 1 = 0$
The limit $\lim \left[ \left\{ 1 - \cos \left( \sin ^ { 2 } a x \right) \right\} / x \right]$ as $x -> 0$\\
(a) Equals 1\\
(b) Equals a\\
(c) Equals 0\\
(d) Does not exist