MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #4 Solution
1. Find the limits of the following problems. Label the limits as or where appropriate. If the limit does not exist, indicate this as DNE.
lim (3x3 x2 1)
(2)
4x2 x
x
2x3
(1)
lim
(3)
5
Name (PRINT):
(First Name)
Student id:
(Last Name)
Mark:
Math 1000 (Calculus I) - Winter 2012/2013
Section 003 (Instructor: Dr. Xiang-Sheng Wang)
Third midterm test
March 21 (Thursday) 12:00-12:50
Instructions:
1. Please write down your name and student i
Name (PRINT):
(First Name)
Student id:
(Last Name)
Mark:
Math 1000 (Calculus I) - Winter 2012/2013
Section 003 (Instructor: Dr. Xiang-Sheng Wang)
First midterm test
January 31 (Thursday) 12:00-12:50
Instructions:
1. Please write down your name and student
Lecture Notes for Math 1000
Dr. Xiang-Sheng Wang
Memorial University of Newfoundland
Oce: HH-2016, Phone: 864-4321
Oce hours: 13:00-15:00 Wednesday, 12:00-13:00 Friday
Email: xswang@mun.ca
Course website: http:/www.ucs.mun.ca/~xiangshengw/1000.html
Lectur
Lecture Notes for Math 1000
Dr. Xiang-Sheng Wang
Memorial University of Newfoundland
Oce: HH-2016, Phone: 864-4321
Oce hours: 13:00-15:00 Wednesday, 12:00-13:00 Friday
Email: xswang@mun.ca
Course website: http:/www.ucs.mun.ca/~xiangshengw/1000.html
Lectur
Lecture Notes for Math 1000
Dr. Xiang-Sheng Wang
Memorial University of Newfoundland
Oce: HH-2016, Phone: 864-4321
Oce hours: 13:00-15:00 Wednesday, 12:00-13:00 Friday
Email: xswang@mun.ca
Course website: http:/www.ucs.mun.ca/~xiangshengw/1000.html
Lectur
Lecture Notes for Math 1000
Dr. Xiang-Sheng Wang
Memorial University of Newfoundland
Oce: HH-2016, Phone: 864-4321
Oce hours: 13:00-15:00 Wednesday, 12:00-13:00 Friday
Email: xswang@mun.ca
Course website: http:/www.ucs.mun.ca/~xiangshengw/1000.html
Lectur
3.4
Optimization problem
Step 1: Assign variables.
Step 2: Find the objective function and determine its domain.
Step 3: Optimize the function.
Example 1. A piece of wire of length L is bent into the shape of a rectangle. Which dimensions produce
the rect
Lecture Notes for Math 1000
Dr. Xiang-Sheng Wang
Memorial University of Newfoundland
Oce: HH-2016, Phone: 864-4321
Oce hours: 13:00-15:00 Wednesday, 12:00-13:00 Friday
Email: xswang@mun.ca
Course website: http:/www.ucs.mun.ca/~xiangshengw/1000.html
Lectur
Bonus questions
1. Use four dierent methods to prove the quotient rule. Each method worths 1 bonus mark.
2. Prove the chain rule. (1 bonus mark)
3. Use two dierent methods to prove
(sec1 x) =
1
|x| x2 1
and
(csc1 x) =
1
|x| x2 1
Each method worths 1 bonus
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #7 Solution
dy
1. Find dx for the following implicit functions.
(1)
ey = sin(x + y)
(2)
xy = cosh x + sinh y
Solution.
(1)
(2)
dy
dy
= cos(x + y) 1 +
dx
dx
cos(x + y)
dy
= y
dx
e cos(x + y)
ey
y+
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #3 Solution
Find the limits of the following problems. Label the limits as or where appropriate. If the limit does not exist, indicate this as DNE.
1
1
|x2 x|
+ 2
lim
lim
(2)
(1)
x0
x x x
x1+ x 1
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #2 Solution
1. Use the graph of y = f (x) below to determine each of the following. Label the limits
as or where appropriate. If the limit does not exist or the value of the function
is undened,
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #1 Solution
x1
1. Simplify f (x) = x1 , where x 0 and x = 1.
Solution. f (x) =
x + 1.
x 1
2. Express f (x) = |1x| as a piecewise-dened function.
cfw_
Solution.
x + 1,
x>1
f (x) =
x 1, x < 1
2
3.
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #5 Solution
1. Use the denition of the derivative to dierentiate each of the following.
1
f (x) =
f (x) = x
(2)
(1)
x1
Solution.
(1)
f (x) = lim
1
x+h1
h0
(2)
h
1
x1
= lim
(x1)(x+h1)
(x+h1)(x1)
h
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #6 Solution
1. Use the denition of the derivative to prove that (cos x) = sin x.
Solution.
cos(x + h) cos x
h
cos x cos h sin x sin h cos x
= lim
h0
h
cos x(cos h 1)
sin x sin h
= lim
lim
h0
h0
Name (PRINT):
(First Name)
Student id:
(Last Name)
Mark:
Math 1000 (Calculus I) - Winter 2012/2013
Section 003 (Instructor: Dr. Xiang-Sheng Wang)
Second midterm test
February 21 (Thursday) 12:00-12:50
Instructions:
1. Please write down your name and stude