Question

why in lecture 1, the area of triangle was only '2' instead of 2XoYo, although from calculation, the second value came out.

Answer 1

A characteristic of this function (y = 1/x) is that for any non-zero value of x, x*y = 1. Therefore, the area of any triangle enclosed by axes and tangent to the function y = 1/x is necessarily 2. Specifically (see video at 40:30):
\[Area = 1/2(2x _{0})(2y _{0})=2\]
because \[x _{0}*y _{0} = 1.\]

Answer 2

Area = 1/2 * base* height
Plugging in the value using the x-intercept for base and y-intercept for height, we get
Area = 1/2* 2xo *2yo = 2xo*yo
We know that the function y = 1/x
Therefore, at the point (xo,yo) or (xo,1/xo), the value of yo = 1/xo
Plugging in the value, we always get the area equals to 2.