(Solved): If a ball is thrown straight up into the air with an initial velocity of 90ft/s, its height in feet ...

If a ball is thrown straight up into the air with an initial velocity of $90\mathrm{ft}/\mathrm{s}$, its height in feet after $t$ second is given by $y=90t?16t^2$. Find the average velocity for the time period beginning when $t=1$ and lasting (i) 0.5 seconds (ii) 0.1 seconds (iii) 0.01 seconds Finally based on the above results, guess what the instantaneous velocity of the ball is when $t=1$. Consider the function $f(x)=\frac{\sin (2x)}{x}$. (a) Fill in the following table of values for $f(x)$ (Enter your answers rounded to within two decimal places.): (b) Based on your table of values, what would you expect the limit of $f(x)$ as $x$ approaches zero to be? ${\lim }_{x?0}\frac{\sin (2x)}{x}=$ (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 0.01 . In other words, find a window of height 0.02 such that the graph exits the sides of the window and not the top or bottom. What is the window? (Enter $x$-values rounded to within four decimal places. All blanks must be filled to receive any credit.)