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Problem 25 Easy Difficulty

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.

$ \displaystyle \lim_{\theta \to 0}\frac{\sin 3\theta}{\tan 2\theta} $

Answer

$$\begin{aligned}
&\text { For } f(\theta)=\frac{\sin 3 \theta}{\tan 2 \theta}\\
&\begin{array}{|l|c|}
\hline \theta & f(\theta) \\
\hline\pm 0.1 & 1.457847 \\
\pm 0.01 & 1.499575 \\
\pm 0.001 & 1.499996 \\
\pm 0.0001 & 1.500000 \\
\hline
\end{array}
\end{aligned}$$
It appears that $\lim _{\theta \rightarrow 0} \frac{\sin 3 \theta}{\tan 2 \theta}=1.5$
The graph confirms that result.

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