As shown in the figure, there is a sector OAB with radius 1 and central angle $\frac { \pi } { 2 }$. Let H be the foot of the perpendicular from point P on arc AB to line segment OA, and let Q be the intersection of line segment PH and line segment AB. When $\angle \mathrm { POH } = \theta$, let $S ( \theta )$ be the area of triangle AQH. What is the value of $\lim _ { \theta \rightarrow 0 + } \frac { S ( \theta ) } { \theta ^ { 4 } }$? (Here, $0 < \theta < \frac { \pi } { 2 }$) [4 points] (1) $\frac { 1 } { 8 }$ (2) $\frac { 1 } { 4 }$ (3) $\frac { 3 } { 8 }$ (4) $\frac { 1 } { 2 }$ (5) $\frac { 5 } { 8 }$
As shown in the figure, there is a sector OAB with radius 1 and central angle $\frac { \pi } { 2 }$. Let H be the foot of the perpendicular from point P on arc AB to line segment OA, and let Q be the intersection of line segment PH and line segment AB. When $\angle \mathrm { POH } = \theta$, let $S ( \theta )$ be the area of triangle AQH.\\
What is the value of $\lim _ { \theta \rightarrow 0 + } \frac { S ( \theta ) } { \theta ^ { 4 } }$? (Here, $0 < \theta < \frac { \pi } { 2 }$) [4 points]\\
(1) $\frac { 1 } { 8 }$\\
(2) $\frac { 1 } { 4 }$\\
(3) $\frac { 3 } { 8 }$\\
(4) $\frac { 1 } { 2 }$\\
(5) $\frac { 5 } { 8 }$