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..........

CPhill
Oct 31, 2015

#4**+5 **

Best Answer

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.

Melody
Oct 31, 2015

#5**0 **

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)

CPhill
Oct 31, 2015