This one should be a little easier than the first Challenge..........!!!
Given the hyperbola y = 1/x with its graph restricted to the first quadrant.......prove that, for any point b on the hyperbola in that quadrant, the triangle with the the vertices (0,0), (b, 1/b), (b, 0 ) always has a constant area........
Part 2.........show that for any point on the hyperbola with an x value of b >1, that the area bounded by the hyperbola, the x axis, the line x = 1 and the line x = b equals ln b
Here's a pic to get you started..........
For the triangle the area is
.5 x b x 1/b = 0.5 which is a constant.
For the second one Area= int of 1/x dx = (ln x ) from 1 to b = lnb
Not much of a challenge CPhill. Hahaha.
Guest....look at the first part of the question, again...it's one side of the triangle whose vertices are (0,0), (b, 1/b) and (b, 0)