When the volume is 10
cubic meters, the depth is 2 meters. As the volume increased from 0 to
10 cubic meters, the depth increased by 2 meters for every cubic meter of
water. When the volume is 10 cubic meters, the depth will increase by 2
meters. As volume varies by a very small amount from 10 cubic meters,
the depth of water increases by 2 times as much as the change in volume.
The instantaneous rate of change of the depth’s value with respect to
volume when the volume is 10 cubic meters is 2 meters per cubic meter.

Please answer each of these questions to the best of your ability. You are welcome to re-watch parts of any of the videos to help you.

Water is flowing into a tank. The function gives the depth of the water in meters
when the volume of the water in the tank is cubic meters. It turns out that .
Which statement best explains the meaning of .

The images below show the graph of a parabola given by . To the right is an image
zoomed in on the point . It turns out that .
After zooming enough to where the graph of appears essentially linear, which
statement best describes the length of the blue vertical vector?

The length of the
blue vector is . The length of the blue vector is . The length of the
blue vector is . The length of the blue vector is times as much as the
value of . The length of the blue vector is times as much as the value
of . The length of the blue vector is times as much as the value of .