Hey, I looked on a graphing calculator and found that the limit of acos(x)-(pi/2) as x goes to 0 equals 0. Here's the only iffy part: is pi/2 a coincidence just popping up as some random number, or does the acos function acually really relate to pi/2?:/
its because acos is the inverse function of the cosine function. The reason pi appears is because we're working with radians.
pi radians = 180 degree's, so pi/2 radians = 90 degrees
cos(90) = 0 so acos(0) = 90. But since we like to work with radians rather then degrees to describe an angle, the angle 90 degrees is rewritten as pi/2 radians.
So acos(0) = pi/2. :-)
Its also cool to note that the limit of tan x as x approaches pi/2 from the left (90 degree's) is infinity. Therefore the limit of atan(x) as x approaches infinity, is pi/2. :-)
A logarithm is just a misspelled algorithm.