calculus 2: Mathematica Project

Name:__________________________Date:____________________Score:____________

Calculus II Project 4 Due Date: December 5, 2018

Directions: Answer each of the questions thoroughly. Show your work to earn full credit.

All work must be typed (no-hand written please!) (5 points each)

1. On of “strange- but true” in mathematics is 0.999999…=1. Use what you know about infinite

series to show that.

2. Suppose that circles of equal diameters are packed tightly in n rows (n-circles in the nth row)

inside an equilateral triangle. If A is the area of the triangle and An is the total area occupied by

the n rows of circles. Show that 32

lim 

  A

A n

n

3. Find the Maclaurin series of and the radius of convergence for the function

)1ln()( xxf 

4. Investigate the family of polar curves given by sin1 cr  . How does the shape change as the value c changes? (These curves are called limacons). You should graph using Mathematica

and for at least 6 various values of c.

5. Sketch the graph of and find the area of the region enclosed by the asteroid whose parametric

equations are given by

 3

cosax  ,  3

sinay 