Question

A particle moves along the x axis so that its position at any time t>= 0 is given by x = arctan t
What is the limiting position of the particle as t approaches infinity?
Answer is pi/2
How do I solve this? Thanks a lot.


You want to find the limit of arctan(t) as t approaches infiniti.

arctan(t) = 1/tan(t)

For our purposes, the denominator of a fraction cannot equal zero.

This should get you started. If you need more help, be specific.


You have x(t)=tan^-1(t)
Since lim x-> pi/2 from the right of tan x =+infinity, lim t->+infinity of arctan t = pi/2
It might help if you looked at the graph of arctan x to see this.