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 th
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
Ins
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
I
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: [email protected]
Course webs
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: [email protected]
Course webs
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: [email protected]
Course webs
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: [email protected]
Course webs
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
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: [email protected]
Course webs
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
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
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
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 d
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 funct
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) =
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
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