Consider the function $f(x)=\frac{sin(2x)}{x}$

$($a$)$ Fill in the following table of values for $f(x)$ :

$\backslash$table$[[x=,-0\mathrm{.}1,-0\mathrm{.}01,-0\mathrm{.}001,-0\mathrm{.}0001,0\mathrm{.}0001,0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1],[f(x)=,,,,,,,,]]$

$($b$)$ Based on your table of values, what would you expect the limit of $f(x)$ as $x$ approaches zero to be$?$

$\underset{x0}{lim}\frac{sin(2x)}{x}=$

$$

$($c$)$ Graph the function to see if it is consistent with your answers to parts $($a$)$ and $($b$).$ By graphing, find an interval for $x$ near zero such that the difference between your conjectured limit and the value of the function is less than $0\mathrm{.}01.$ In other words, find a window of height $0\mathrm{.}02$ such that the graph exits the sides of the window and not the top or bottom. What is the window?

$$

$$

$y$

Consider the function $f(x)=\frac{sin(2x)}{x}$

$($a$)$ Fill in the following table of values for $f(x)$ :

$\backslash$table$[[x=,-0\mathrm{.}1,-0\mathrm{.}01,-0\mathrm{.}001,-0\mathrm{.}0001,0\mathrm{.}0001,0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1],[f(x)=,,,,,,,,]]$

$($b$)$ Based on your table of values, what would you expect the limit of $f(x)$ as $x$ approaches zero to be$?$

$\underset{x0}{lim}\frac{sin(2x)}{x}=$

$$

$($c$)$ Graph the function to see if it is consistent with your answers to parts $($a$)$ and $($b$).$ By graphing, find an interval for $x$ near zero such that the difference between your conjectured limit and the value of the function is less than $0\mathrm{.}01.$ In other words, find a window of height $0\mathrm{.}02$ such that the graph exits the sides of the window and not the top or bottom. What is the window?

$$

$$

$y$