Question

use a calculator in radian mode to complete the following table. (round to four decimal places as needed.)
0 0.5 0.4 0.2 0.1 0.01 0.001 0.0001
-3 tan θ
-1.6389 -1.2684 -0.6081 -0.3010
f(θ) = -\frac{3 tan θ}{θ}
-3.2778 -3.1709 -3.0407 -3.0100
use a calculator in radian mode to complete the following table. what can be concluded about the value of f(θ)= -\frac{3 tan θ}{θ} as θ approaches 0?

Explanation:

Step1: Calculate for \(\theta = 0.001\)

First, find \(-3\tan(0.001)\approx - 0.003\). Then \(f(0.001)=\frac{-3\tan(0.001)}{0.001}\approx\frac{- 0.003}{0.001}=-3.0000\)

Step2: Calculate for \(\theta = 0.0001\)

Find \(-3\tan(0.0001)\approx - 0.0003\). Then \(f(0.0001)=\frac{-3\tan(0.0001)}{0.0001}\approx\frac{- 0.0003}{0.0001}=-3.0000\)

Answer:

The completed table for the second row (values of \(f(\theta)\)): \(-3.0000\), \(-3.0000\) (for \(\theta = 0.001\) and \(\theta=0.0001\) respectively). As \(\theta\) approaches \(0\), we can conclude that \(\lim_{\theta
ightarrow0}\frac{-3\tan\theta}{\theta}=- 3\)