A particle moves along the x-axis so that its position at any time t is greater than or equal to 0 is given by x=arctan(t).
a. Prove that the particle is always moving to the right
b. Prove that the particle is always decelearating
c.What is the limit of the position of the particle as t approaches infinity?

I know the derivative of the inverse trig function is 1/1+t^2, but how do i prove the a, b, and c.

Question

A particle moves along the x-axis so that its position at any time t is greater than or equal to 0 is given by x=arctan(t).
a. Prove that the particle is always moving to the right
b. Prove that the particle is always decelearating
c.What is the limit of the position of the particle as t approaches infinity?

I know the derivative of the inverse trig function is 1/1+t^2, but how do i prove the a, b, and c.