Q. 42 - Calculus

Question

Evaluate the limits in Exercises 42–45.

$\underset{t\to 0}{lim}(\sin 3t, \cos 3t)$

Step-by-Step Solution

Answer

The evaluation of the limit $\underset{t\to 0}{lim}(\sin 3t, \cos 3t)$ is $j$.

Step 1. Given Information.

The function:

$\underset{t\to 0}{lim}(\sin 3t, \cos 3t)$

Step 2. Apply the limits.

By applying the limit and solving,

$$\begin{gathered} \underset{t\to 0}{lim}(\sin 3t, \cos 3t)=\underset{t\to 0}{lim} (\sin 3t)i+\underset{t\to 0}{lim}(\cos 3t)j \\ =0i+1j \\ =j \end{gathered}$$