Evaluate the following limits: (b) t 0 ( 3t)/(t) (c) x infinity ^-1((x-1)/(2x))

The limit is of the form $\lim_{x \to 0} \frac{\sin ax}{x} = a$.

In this case, $a=3$.

The final answer is $\boxed{3}$.

Let $L = \lim_{x \to \infty} \frac{x-1}{2x}$.
To evaluate this limit, divide both the numerator and the denominator by the highest power of $x$, which is $x$:

As $x \to \infty$, $\frac{1}{x} \to 0$.

Since $\cos^{-1}(y)$ is a continuous function for $y \in [-1, 1]$, we can write:

The value $y$ such that $\cos y = \frac{1}{2}$ in the principal range $[0, \pi]$ is $\frac{\pi}{3}$.

The final answer is $\boxed{\frac{\pi}{3}}$.