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Q. 43

Expert-verifiedFound in: Page 860

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Evaluate the limits in Exercises 42–45.

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

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

The function:

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

By applying the limit and solving,

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

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