## Related questions with answers

(a) Investigate $\lim _{x \rightarrow 0} \cos \frac{\pi}{x}$ by using a table and evaluating the function $f(x)=\cos \frac{\pi}{x}$ at $x=-\frac{1}{2},-\frac{1}{4},-\frac{1}{8},-\frac{1}{10},-\frac{1}{12}, \ldots, \frac{1}{12}, \frac{1}{10}, \frac{1}{8}, \frac{1}{4}, \frac{1}{2}$. (b) Investigate $\lim _{x \rightarrow 0} \cos \frac{\pi}{x}$ by using a table and evaluating the function $f(x)=\cos \frac{\pi}{x}$ at $x=-1,-\frac{1}{3},-\frac{1}{5},-\frac{1}{7},-\frac{1}{9}, \ldots, \frac{1}{9}, \frac{1}{7}, \frac{1}{5}, \frac{1}{3}, 1$. (c) Compare the results from (a) and (b). What do you conclude about the limit? Why do you think this happens? What is your view about using a table to draw a conclusion about limits? (d) Use technology to graph f. Begin with the x -window $[-2 \pi, 2 \pi]$ and the y-window [-1,1]. If you were finding $\lim _{x \rightarrow 0} f(x)$ using a graph, what would you conclude? Zoom in on the graph. Describe what you see.

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