MATH1003
ASSIGNMENT 4
ANSWERS
1.
(i)
dy
= 1 f (x) + x f (x)
dx
= f (x) + xf (x).
(ii)
dy
f (x) x f (x) 1
=
dx
x2
f ( x) f ( x)
=
2.
x
x
(iii)
dy
= 2xf (x) + x2 f (x).
dx
(iv)
dy
(f (x) + xf (x) x (1/2)(1 + xf (x)x1/2
=
,
dx
x
(f (x) + xf (x)x (1/2)(1 + x
MATH 1003 1B Winter 2015
Assignment # 3
Answer the following questions. Be sure to include your workings. Be clear and explain your steps. You can discuss the
assignment questions and course material with other students and with the instructor but you mus
MATH 1003 1B Winter 2015
Assignment # 7
Answer the following questions. Be sure to include your workings. Be clear and explain your steps. You can discuss the
assignment questions and course material with other students and with the instructor but you mus
Instructors Name
Students Name (Print)
Students Signature
Student Number
THE UNIVERSITY OF NEW BRUNSWICK
Saint John
Math 1003
Canada
Final Exam
April 28, 2014
FOR GRADING ONLY
INSTRUCTIONS
Page
1. Do not unstaple the exam or detach
any pages.
MARK
2
16
2.
MATH 1003 1B Winter 2015
Assignment # 5
Answer the following questions. Be sure to include your workings. Be clear and explain your steps. You can discuss the
assignment questions and course material with other students and with the instructor but you mus
MATH 1003
Name [please print]
Instructor: Dr. R. McKay TEST #1 Version: a
Student Number
February 25th, 2014
SHOW ALL WORK-Test length 50 minutes, maximum mark
[6mk]
40
41
40 .
1. (a) What is the domain of f (x) = ln(2 x)? Write your answer in interval no
FREDERICTON
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF NEW BRUNSWICK
STAT 2593: STATISTICS AND PROBABILITY FOR ENGINEERS
ASSIGNMENT # 3
Student Name:
Student ID:
Section:
Notes:
1. Due in Class on
Monday, February 01, 2016 for Section # FR01B
MATH 1003 1B Winter 2015
Assignment # 4
Answer the following questions. Be sure to include your workings. Be clear and explain your steps. You can discuss the
assignment questions and course material with other students and with the instructor but you mus
Department of Mathematics and Statistics
University of New Brunswick, hedericton
Math 1823 Final Examination — April 2003
Time: 3 hours
J USTIFY YOUR ANSWERS
1. (6 marks] Evaluate the following limits:
(3.) um 3x3+cc+1
x—mc —$3+3;2+7
(manE_1
:n—rl 33—1
MATH1003
ASSIGNMENT 10
ANSWERS
1. Let x and d denote the lengths of the sides, in meters, of the rectangle. Then:
xd = 1000,
1000
.
x
The perimeter is given by P (x) = 2x + 2d = 2(x + 1000/x). We wish to minimise
P (x).
2000
dP
=2 2 .
dx
x
The derivative
Math 1003
Fall 2003 Midterm Solutions
x2
1. Let f (x) = x
x+1
x<0
0x1
x>1
(a) Sketch the graph of f . What is the range of f .
You should ll lable the axes and ll put tics on them to indicate the scale. The range
of f is all real numbers except those in t
MATH1003
ASSIGNMENT 3
ANSWERS
1.
(i) We can factorise the numerator:
x2 81 = (x 9)(x + 9) = ( x 3)( x + 3)(x + 9).
Hence:
x2 81
= ( x + 3)(x + 9).
x3
Thus the limit is (3 + 3) (9 + 9) = 108.
(ii) Recall that:
x,
when x 0;
x, when x < 0.
|x| =
Since x 1 we
MATH1003
ASSIGNMENT 1
ANSWERS
x
. Then:
x+1
2+h
(i) f (2 + h) =
3+h
x+h
(ii) f (x + h) =
x+h+1
f (x + h) f (x)
1
(iii)
=
.
h
(x + 1)(x + h + 1)
1. Let f (x) =
2. As a rational function, the function is dened whenever the denominator is nonzero. Since x2 +
MATH1003
ASSIGNMENT 5
ANSWERS
1.
(i)
d
d1
1d
sec x =
= 2
cos x
dx
dx cos x
cos x dx
1
=
sin x
cos2 x
= sec x tan x.
(ii)
x2
y=
cos x
= x2 sec x
dy
= 2x sec x + x2 sec x tan x
dx
= x sec x(2 + x tan x).
(iii)
dy
d
= sec x tan x (x cot x) + sec x (x cot x)
MATH1003
ASSIGNMENT 6
ANSWERS
1. Let g (x) + x sin g (x) = x2 , and g (1) = 0. Dierentiating both sides we obtain:
g (x) + sin g (x) + xg (x) cos g (x) = 2x.
Setting x = 1 gives:
g (1) + sin 0 + g (1) = 2.
Rearranging we see that g (1) = 1. Dierentiating
MATH1003
ASSIGNMENT 9
ANSWERS
1. Let f : [0, 2] R be given by f (x) = x3 + x 1. This is continuous on the given
interval and, since f is a polynomial, dierentiable on (0, 2). Hence it satises the
conditions of the Mean Value Theorem.
The Mean Value Theore
MATH1003
ASSIGNMENT 8
ANSWERS
1. Be careful! Since 1 sin 0 and csc 1 as /2, LHpitals Rule does
o
not apply. But this isnt a problem, since we need only use the Laws of Limits:
1 sin
0
=
/2
csc
1
lim
= 0.
2. Proposition. For any > 0,
lim
x
ln x
=0
x
Proo
DEPARTMENT OF MATHEMATICS & STATISTICS
MATH 1823
FINAL EXAMINATIQE TIME: 3 HOURS
APRIL 2005 TOTAL POINTS : 85
NO CALCULATORS
MARKS
(9) 1. Calculate the following limits:
;I;2 i 61‘ + 8
c l' ————————
(1) :1; — 2
. 2 2
(b) hm 9:1: »« — — 4
m 44 :17
( ) 1,