MATH138 Final: MATH138 Final Exam 2013 Winter
15 Oct 2018
School
Department
Course
Professor
Last name (Print): First name (Print):
UW Student ID Number:
Your course section number (see below):
University of Waterloo
Final Examination
Math 138
(Calculus II )
Instructor: See table below Section: See table below
Date: Monday April 15, 2013 Time: 9:00-11:30 a.m.
Term: 1131 Duration of exam: 2 hours 30 minutes
Number of exam pages: 11 Exam type: Closed Book
(including cover page)
Additional materials: “Pink tie” calculators
Circle your instructor’s name and section number
Instructor Section
K. Miller 001
A. Popov 002
S. Speziale 003
D. Park 004
K. Purbhoo 005
D.E. Chang 006
F. Vinette 008
S. Speziale 009
Formulas
•sin 2α= 2 sin αcos α
•sin2α= (1 −cos 2α)/2
•cos2α= (1 + cos 2α)/2
•sin2α+ cos2α= 1
•tan2α+ 1 = sec2α
Instructions
1. Write your name and ID number at the top
of this page. Please circle your instructor’s
name and your section number up above.
2. Answer the questions in the spaces provided,
using the backs of pages for overflow or
rough work.
3. Show all work required to obtain your
answers. Your grade will be influenced
by how clearly you express your ideas,
and how well you organize your solu-
tions.
Question Mark
1 /10
2 /8
3 /12
4 /10
5 /10
6 /11
7 /8
8 /9
9 /8
Total /86
Last name (Print): First name (Print):
UW Student ID Number:
Your course section number (see below):
University of Waterloo
Final Examination
Math 138
(Calculus II )
Instructor: See table below Section: See table below
Date: Monday April 15, 2013 Time: 9:00-11:30 a.m.
Term: 1131 Duration of exam: 2 hours 30 minutes
Number of exam pages: 11 Exam type: Closed Book
(including cover page)
Additional materials: “Pink tie” calculators
Circle your instructor’s name and section number
Instructor Section
K. Miller 001
A. Popov 002
S. Speziale 003
D. Park 004
K. Purbhoo 005
D.E. Chang 006
F. Vinette 008
S. Speziale 009
Formulas
•sin 2α= 2 sin αcos α
•sin2α= (1 −cos 2α)/2
•cos2α= (1 + cos 2α)/2
•sin2α+ cos2α= 1
•tan2α+ 1 = sec2α
Instructions
1. Write your name and ID number at the top
of this page. Please circle your instructor’s
name and your section number up above.
2. Answer the questions in the spaces provided,
using the backs of pages for overflow or
rough work.
3. Show all work required to obtain your
answers. Your grade will be influenced
by how clearly you express your ideas,
and how well you organize your solu-
tions.
Question Mark
1 /10
2 /8
3 /12
4 /10
5 /10
6 /11
7 /8
8 /9
9 /8
Total /86
Math 138 Final Exam, Winter 2013 Page 2 of 11 Name:
1. Evaluate the following integrals.
(a) Z1
0
xarctan x dx[5]
(b) Z2x−1
x2(x2+ 1) dx[5]
2
Document Summary
Number of exam pages: 11 (including cover page) Instructor section: miller, popov, speziale, park, purbhoo. Formulas: sin 2 = 2 sin cos , sin2 = (1 cos 2 )/2, cos2 = (1 + cos 2 )/2, sin2 + cos2 = 1, tan2 + 1 = sec2 . Instructions: write your name and id number at the top of this page. Please circle your instructor"s name and your section number up above: answer the questions in the spaces provided, using the backs of pages for over ow or rough work, show all work required to obtain your answers. Your grade will be in uenced by how clearly you express your ideas, and how well you organize your solu- tions. Name: initially there is 10 kg of salt in a tank containing 500 l of salt-water solution. Pure water enters the tank at a rate of 10 l/min, and the solution is drained at 5 l/min.
