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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} $

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

02:53

Daniel J.

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

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