Chapter 4.6, Problem 37ES

Let $s=\sqrt{2t^2+1}$ be the position function of a particle moving along a coordinate line.

(a) Use a graphing utility to generate the graph of $\upsilon$ versus $t,$ and make a conjecture about the velocity of the particle as $t\to +\infty$ .

(b) Check your conjecture by finding $\underset{t\to +\infty }{\lim }\upsilon$ .