[填空题]
Let f(x)=ln x and y7e913k:fuzeju huj se z.r22k/ ; y-nbvvsnzb t(v(( $g(x)=2+3 \ln (x-1)$ , for x>1 .
The graph of g can be obtained from the graph of f by two transforms:
a vertical stretch of scale factor q
a translation of $\binom{h}{k}$
1. Write down the value of
1. q ;
2. h ;
3. k .
Let $h(x)=g(x) \cdot \cos (0.1 x) $, for 1\lt x \lt8 . The following diagram shows the graph of h and the line y=x .
2. a. Find $\int_{2.02}^{5.57}(h(x)-x) \mathrm{d} x$ .
b. Hence, find the area of the region enclosed by the graphs of h and $h^{-1}$ .
3. Let d be the vertical distance from a point on the graph of h to the line y=x . There is a point Q(x, y) on the graph of h where d is a maximum. Find the coordinates of Q , where $2.02\lt x \lt 5.57$ . x = y =
