## Calculus (3rd Edition)

Since the function $g(t)=\frac{t}{t+1}$ is continuous on $[0,1]$ and $g(0)=0\neq g(1)=0.5$ and $0.499$ is between $g(0)$ and $g(1)$, then by the Intermediate Value Theorem the function $g(t)$ takes on the value $0.499$ for some $t\in (0,1)$.