At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To evaluate the limit [tex]\(\lim _{x \rightarrow 0} \frac{\sin 3 x}{x}\)[/tex] using given values of [tex]\(x\)[/tex], we can set up a table with the corresponding values of [tex]\(\frac{\sin 3 x}{x}\)[/tex].
[tex]\[ \begin{array}{|c|c|c|c|} \hline x & \frac{\sin 3 x}{x} & x & \frac{\sin 3 x}{x} \\ \hline -0.1 & 2.95520207 & 0.1 & 2.95520207 \\ \hline -0.01 & 2.99955002 & 0.01 & 2.99955002 \\ \hline -0.001 & 2.99999550 & 0.001 & 2.99999550 \\ \hline -0.0001 & 2.99999996 & 0.0001 & 2.99999996 \\ \hline \end{array} \][/tex]
Based on the table, as [tex]\(x\)[/tex] approaches 0 from both the negative and positive sides, the value of [tex]\(\frac{\sin 3 x}{x}\)[/tex] gets closer to approximately 3. Consequently, we can estimate that
[tex]\[ \lim _{x \rightarrow 0} \frac{\sin 3 x}{x} \approx 3. \][/tex]
[tex]\[ \begin{array}{|c|c|c|c|} \hline x & \frac{\sin 3 x}{x} & x & \frac{\sin 3 x}{x} \\ \hline -0.1 & 2.95520207 & 0.1 & 2.95520207 \\ \hline -0.01 & 2.99955002 & 0.01 & 2.99955002 \\ \hline -0.001 & 2.99999550 & 0.001 & 2.99999550 \\ \hline -0.0001 & 2.99999996 & 0.0001 & 2.99999996 \\ \hline \end{array} \][/tex]
Based on the table, as [tex]\(x\)[/tex] approaches 0 from both the negative and positive sides, the value of [tex]\(\frac{\sin 3 x}{x}\)[/tex] gets closer to approximately 3. Consequently, we can estimate that
[tex]\[ \lim _{x \rightarrow 0} \frac{\sin 3 x}{x} \approx 3. \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.