MATH 136-04, Advanced Placement Calculus

Homework Assignment #5

Due Friday, October 13, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Single Variable Calculus, Concepts and Contexts 3rd ed., the required text for the course. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.
Important: Please list the names of any students or faculty who you worked with on the assignment.

Section 4.2, pp. 274 - 277
Problems:   4, 5, 23, 31, 37, 48

Section 4.3, pp. 286 - 289
Problems:   1, 9, 12, 20, 29

Section 4.5, pp. 303 - 305
Problems:   6, 7, 15, 17, 26, 33

Hint: In problem #33, try factoring out an x first before taking the limit.

Section 4.6, pp. 311 - 315
Problems:   4, 12, 21, 24, 32

Hint: In problem #24, you will need to look up (or derive!) the volume V and surface area S of a standard cone (with circular base.) For example, you could try Wolfram's Mathematical Encyclopedia . Then, minimize the square of the surface area S^2 to avoid square roots. This works because S is always positive and the squaring function is increasing. In other words, wherever S^2 attains a minimum, S will as well.