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Q. 43

Expert-verified
Found in: Page 860

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# Evaluate the limits in Exercises 42–45.$\underset{t\to \mathrm{\pi }}{lim}\left(\mathrm{sin}t,\mathrm{cos}t,sect\right)$

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

See the step by step solution

## Step 1. Given Information.

The function:

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

## Step 2. Apply the limits.

By applying the limit and solving,

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

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