MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Mathematics 1001
Assignment 1
Winter 2016
SOLUTIONS
[4]
[4]
[4]
[4]
[4]
[4]
[4]
[4]
Z
Z
1
8
2
3
2x2 + x 3 8x5 dx
2x + x 5 dx =
1. (a)
x
3 4
1 4
2
2
1 3
3 4
+ C = x3 + x 3 + 4
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Basic Integration
Math 1001 Worksheet
Winter 2016
For practice only. Not to be submitted.
1. Evaluate each of the following integrals using any combination of elementary integral
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1000
Assignment 6
Fall 2015
SOLUTIONS
[4]
1. (a) We use the Product Rule, followed by the Chain Rule:
f 0 (x) = [cos(x)]0 log5 (cos(x) + cos(x)[log5 (cos(x)]0
= sin(x) log5
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 7
MATH 1000
Fall 2015
SOLUTIONS
[4]
1. First we have
s(t) = At3 + Bt2 + Ct + D
v(t) = s0 (t) = 3At2 + 2Bt + C
a(t) = s00 (t) = 6At + 2B.
We know that s(0) = 0, so D =
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1000
Assignment 5
Fall 2015
SOLUTIONS
[4]
1. (a) We use the Quotient Rule:
f 0 (x) =
[4]
=
[1 + sin(x)][x + cos(x)] [x cos(x)][1 sin(x)]
[x + cos(x)]2
=
2x sin(x) + 2 cos(x)
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1000
Test 2
Fall 2015
SOLUTIONS
[12]
1. First we consider values of x for which f (x) is undefined.
The first part of the definition will be undefined if x + 5 = 0, so x = 5
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1000
Assignment 4
Fall 2015
SOLUTIONS
[8]
1. (a) We have
f (x + h) f (x)
h0
h
x+h+1
x+1
x3
x+h3
= lim
h0
h
(x + h + 1)(x 3) (x + 1)(x + h 3)
1
= lim
h0
(x 3)(x + h 3)
h
f 0
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
TEST 2
Name
[12]
MATH 1000
October 30th, 2015
MUN Number
1. Consider the function
2
x + 7x + 10
, for x < 3
x + 5
13 x,
for x = 3
f (x) =
2x 1
,
for x > 3
16 x2
Use the definit
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1000
Test 3
SOLUTIONS
[5]
1. (a) We use the Product Rule, followed by the Chain Rule:
d 3
d
dy
=
[x ] sin(ex ) + [sin(ex )]x3
dx
dx
dx
d
= 3x2 sin(ex ) + cos(ex ) [ex ]x3
dx
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
TEST 3
Name
MATH 1000
November 20th, 2015
MUN Number
1. Differentiate each of the following functions. Make any obvious simplifications.
[5]
(a) y = x3 sin(ex )
[5]
(b) y = sin(x
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Improper Integrals
Math 1001 Worksheet
Winter 2016
For practise only. Not to be submitted.
1. Determine whether each of the following improper integrals converges or diverges, fi
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Differential Equations
Math 1001 Worksheet
Winter 2016
For practise only. Not to be submitted.
1. Find a particular solution to each differential equation.
(a) f 0 (x) cos(2x 1)
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Limits of Riemann Sums
Math 1001 Worksheet
Winter 2016
For practice only. Not to be submitted.
1. Write each of the following sums using sigma notation.
4
8
16
4096
2
+
+
+
+ +
1
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Area Between Curves
Math 1001 Worksheet
For practice only. Not to be submitted.
1. Find the area of the region bounded by the given curves.
1
and y = 2, on [1, 2]
x2
(b) y = x2 +
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Mathematics 1001
Assignment 4
Winter 2016
SOLUTIONS
[4]
1. (a) Each term of the sum is 3 larger than a perfect square:
4 = (12 + 3),
7 = (22 + 3),
12 = (32 + 3),
19 = (42 + 3), .
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Math 1001 Worksheet
Volumes
Winter 2016
For practise only. Not to be submitted.
1. Use the disc-washer method to find the volume of the solid generated by rotating the indicated
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1001
Test 2
Winter 2016
SOLUTIONS
[8]
1. (a) We use a regular partition with subintervals of width
x =
1
2
(1)
3
=
.
n
2n
We choose the sample point
xi = 1 + ix = 1 +
3i
.
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATH 1001
Test 1
Winter 2016
SOLUTIONS
[5]
[5]
1. (a) We can rewrite the integral as
Z 2
Z
Z 2
x
16
x + 16
dx =
dx +
dx
8x
8x
8x
Z
Z
1
1
=
x dx + 2
dx
8
x
1
= x2 + 2 ln|x| + C.
1
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Assignment 2
Mathematics 1001
Winter 2016
SOLUTIONS
[5]
1. (a) Let u =
1
1
1
so du = 2 dx and du = 2 dx. The integral becomes
x
x
x
Z 1
Z
ex
dx = eu du
x2
= eu + C
1
= e x + C.
[
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Growth and Decay
Math 1001 Worksheet
Winter 2016
For practise only. Not to be submitted.
1. The half-life of Einsteinium-254 is 270 days. A sample initially has a mass of 3 mg.
(
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Integration Strategies
Math 1001 Worksheet
Winter 2016
For practise only. Not to be submitted.
1. The following integrals could use any of the techniques that weve introduced in
MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
Mathematics 1001
Assignment 5
Winter 2016
SOLUTIONS
[5]
[5]
1. (a) This is an elementary integral:
Z 2
Z 2 2
Z
Z
2x 9x + 1
2 2
1 21
dx =
x dx 3
dx +
dx
3x
3 1
3 1 x
1
1
h i2 1 h
Name _
Course/Section _
USE PENCIL PLEASE
Math 110/111 - Term Test 1
18 October 2012
Value: 50 marks
1.
Time Allowed: 90 minutes
. Circle the one best answer for each question below.
Let
A. What type of function is
?
(a) exponential
(b) linear
B. What is
Name _
USE PENCIL PLEASE
Math 110/111 - Term Test 2
22 November 2012
Value: 50 marks
1.
Time Allowed: 75 minutes
Find the derivatives of the functions given below using the differentiation rules. You do NOT
need to simplify your answers, but use GOOD FORM
Defining the Limit (Sections 2.2 and 2.3)
Intuitive Definition: Suppose f ( x ) is defined near c on both sides, except possibly
at c itself. Then
lim f ( x) = L
xc
if f ( x ) is arbitrarily close to L whenever x is sufficiently close to c BUT
not necessa
Definitions and Theorems from Sections 4.1 and 4.2
SECTION 4.1 (and much of Chapter 4) is concerned with the maximum and minimum values of a function,
also called the extreme values or extrema.
Definition: Let f be a function with domain D, and let c be a
Two Applied Optimization Problems
1.
A hockey team expects to sell 6000 tickets for one of its home games at the current price of $20
per ticket, and market research indicates that 200 fewer tickets will be sold for each $1 increase
in the ticket price. D
Limit Laws/Theorems (Section 2.2)
Suppose that c is a real number and that the limits lim f ( x ) and lim g ( x) exist.
x c
xc
Then
1. sum law:
2. difference law:
lim [ f ( x ) + g ( x )] = lim f ( x ) + lim g ( x ) .
x c
x c
xc
lim [ f ( x ) g ( x )] = l