[填空题]
Consider the function ss3gr7+)zna r f defined bkju;o+;q30pq3c2t+iyx 9o c ef wwfg9y $ f(x)=2 \ln (24-1.5 x) $ for x<16 .
The line $L_{1}$: y=x intersects the graph of f at point P .
The line $ L_{2}$ is perpendicular to $ L_{1}$ and tangent to the graph of f at point Q .
1. Find the x -coordinate of point P , to three significant figures. ≈
2. a. Find the exact coordinates of point Q . x = y =
b. Show that the equation of $L_{2} $ is $ y=-x+2 \ln 3+14$ . y =
The shaded region A , as shown in the previous diagram, is enclosed by the graph of f , the line $L_{1}$ and the line $ L_{2}$
3.a. Find the exact x -coordinate of the point where $ L_{2}$ intersects $ L_{1}$ .
b. Hence, find the area of A , to two decimal places.≈
The line $L_{2}$ is also tangent to the graph of the inverse function $f^{-1}$ .
$\text { 4. Find the shaded area enclosed by the graphs of } f, f^{-1} \text { and the line } L_{2} \text {. }$
