Answer to Question #246051 in Calculus for Marie

Question

Let 𝑔(𝜃) = sin 𝜃 𝜃

a) Make a table of the values of g at values of u that approach 𝜃0 = 0 from above and below. Then estimatelim 𝑔(𝜃)

𝜃→0

b) Support your conclusion in part (a) by graphing g near 𝜃0 = 0

Answer 1

a)

$g(\theta)=\dfrac{\sin \theta}{\theta}$

$$\def\arraystretch{1.5} \begin{array}{c:c} \theta & \dfrac{\sin \theta}{\theta} \\ \hline -0.1 & 0.9983341665 \\ \hline -0.01 & 0.9999833334 \\ \hline -0.001 & 0.9999998333 \\ \hline -0.0001 & 0.9999999983 \\ \hline 0.0001 & 0.9999999983 \\ \hline 0.001 & 0.9999998333 \\ \hline 0.01 & 0.9999833334 \\ \hline 0.1 & 0.9983341665 \\ \hline \end{array}$$

$$\lim\limits_{\theta\to 0}\dfrac{\sin \theta}{\theta}=1$$

b)