Math 1210-001
Homework 4
Due 17 June, 2013
This homework assignment is designed to go along with sections 2.7 through
2.9 of your textbook, which we have completed in class. The majority of
your score will be based on how you organize and demonstrate the process of
solving each problem. To that end, make sure your work is neat, legible,
well-organized and self-explanatory. You must staple your assignment to
receive full credit.
Name:
1. (10 points) Assuming that the equation y 2 − x2 = 1 defines a differentiable function of
x, find Dx y by implicit differentiation. (The graph of this function is a hyperbola, which
is one type of cross section of a circular cone.)
2. (10 points) A student is using a straw to drink a milkshake from a conical glass, whose
axis is vertical, at a rate of 3 cubic centimeters per second. If the height of the glass is
10 centimeters and the diameter of the opening is 6 centimeters, how fast is the level of
the liquid falling when the depth of the liquid is 5 centimeters?
3. (10 points) The outside diameter of a soccer ball is 22 cm. If the ball is 0.2 cm thick,
use differentials to approximate the volume of the interior of the ball. (Note: This can
be done without differentials. You must use differentials to receive credit.)