Question

Evaluate the limits in Exercises 42–45.

$\underset{t\to \mathrm{\pi }}{lim}(\sin t,\cos t,sect)$

Short answer

The evaluation of the limit $\underset{t\to \mathrm{\pi }}{lim}(\sin t,\cos t,sect)$is $(0,-1,-1)$.

Step-by-step solution

Step 1. Given Information.

The function:

$\underset{t\to \mathrm{\pi }}{lim}(\sin t,\cos t,sect)$

Step 2. Apply the limits.

By applying the limit and solving,

$$\begin{gathered} \underset{t\to \mathrm{\pi }}{lim}(\sin t,\cos t,sect)=\underset{t\to \mathrm{\pi }}{lim}\left(\sin t\right)i+\underset{t\to \mathrm{\pi }}{lim}\left(\cos t\right)j+\underset{t\to \mathrm{\pi }}{lim}\left(sect\right)k \\ =\mathrm{sin\pi }i+\mathrm{cos\pi }j+sec\mathrm{\pi k} \\ =0\mathrm{i}-\mathrm{j}-\mathrm{k} \\ =(0,-1,-1) \end{gathered}$$