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18.01 Single Variable Calculus
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Fall 2006
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MIT 18.01 Single Variable Calculus Problem Set 6, Study notes of Mathematics
A problem set for mit's 18.01 single variable calculus course, due on november 9, 2006. It includes problems covering topics such as volumes by disks and shells, average value, probability, numerical integration, and trigonometric integrals. Students are expected to work on most of the problems before the exam 3 on november 7, 2006.
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MIT OpenCourseWare http://ocw.mit.edu
18.01 Single Variable Calculus
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Fall 2006
18.01 Problem Set 6
Due THURSDAY 11/09/06, 12:55 pm
Warning: This problem set is due on a THURSDAY not Friday, because of the Veterans’ Day holiday. It is due before lecture, which is at 1:05 on Thursday.
Even though this problem set is due two days after Exam 3, you will need to do most of it by Tuesday, in the process of preparing for Exam 3 — all except the Part I problems connected to Lecture 25.
Part I (22 points)
Lecture 22. Fri. Oct. 27 Volumes by disks and shells. Read: 7.4 Work: 4B-2eg, 5; 4C-1a, 2, 3 4J-
Lecture 23. Tues. Oct. 31 Work; average value; probability. Read: 7.7, to middle p. 247 Notes AV. Work: 249/5, 6, 15 (solutions posted at web site); 4D-2, 3, 5
Lecture 24. Thurs. Oct. 29 Numerical Integration. Read 10.9 Work: 3G-1ad, 4
Lecture 25. Fri. Nov. 3 Trigonometric integrals. Direct substitution. Read 10.2, 10.3 Work: 5B-9, 11, 13, 16; 5C-5, 7, 9, 11 (due after Exam 3)
Lecture 26. Tues. Nov. 7 Exam 3 1:05-1:55 covering lectures 18–24.
Part II (30 points)
Directions: Attempt to solve each part of each problem yourself. If you collaborate, solutions must be written up independently. It is illegal to consult materials from previous semesters. With each problem is the day it can be done.
- (not until due date; 3 pts) Write the names of all the people you consulted or with whom you collaborated and the resources you used, or say “none” or “no consultation”. (See full explanation on PS1).
- (Lec 22, 7pts: 3 + 4) Do 7.4/12 and 13.
- (Lec 23, 4pts) The voltage V of house current is given by
V (t) = C sin(120πt)
where t is time, in seconds and C is a constant amplitude. The square root of the average value of V 2 over one period of V (t) (or cycle) is called the root-mean-square voltage, abbreviated RMS. This is what the voltage meter on a house records. For house current, find the RMS in terms of the constant C. (The peak voltage delivered to the house is ±C. The units of V 2 are square volts; when we take the square root again after averaging, the units become volts again.)