MATH 103 200710 Quiz 1
Edward Doolittle Thursday, February 1, 2007
Please do both of the following problems. Each problem is worth 10 marks. You have 20 minutes to finish the quiz. 1. A company manufactures and sells widgets. The company has a fixed cost
MATH 103001
Winter 2013
Solution to Quiz 3
1. (4 marks) Find the equation of the line that is tangent to the graph of the function
f (x) = x + 1 where x = 1.
Solution. f (x) = (x1/2 + 1) = 1 x1/2 . So f (1) = 1 . Note also that f (1) = 2. The
2
2
equation
MATH 103001
Winter 2013
Solution to Quiz 1
1. (3 marks) Given
f (x) =
2x + 1
x2 3
if x 2
if x > 2
nd f (1), f (2) and f (3).
Solution. f (1) = 2 1 + 1 = 1. f (2) = 2 2 + 1 = 3. f (3) = 32 3 = 6.
2. (2 marks) Determine the domain of the function
2t 1
.
f (
MATH 103001
Winter 2013
Solution to Assignment 1
Section 1.1
4. Given f (x) = x/(x2 + 1), nd f (2), f (0), and f (1).
Solution. f (2) = 2/(22 + 1) = 2/5. f (0) = 0/(02 + 1) = 0. f (1) = (1)/(1)2 +
1) = 1/2.
10. Given
h(x) =
2x + 4
x2 + 1
if x 1
if x > 1
n
MATH 103001
Winter 2013
Solution to Assignment 5
Section 3.4
For problems 1, 3, 5, 9, nd the absolute maximum and absolute minimum of the given
function on the specied interval.
1. f (x) = x2 + 4x + 5;
3 x 1
Solution. f (x) = 2x + 4. f (x) = 0 when x = 2.
MATH 103001
Winter 2013
Solution to Assignment 6
Section 3.5
9. A city recreation department plans to build a rectangular playground having an area
of 3,600 square meters and surround it by a fence. How can this be done using the
least amount of fencing?
MATH 103001
Winter 2013
Solution to Assignment 3
Section 2.2
For problems 7, 14, 18, 20, 25, dierentiate the given function. Simplify your answers.
7. y = 2x.
1
Solution. y = 2x1/2 . y = 2 2 x1/2 = 1 .
2x
1
1
14. f (x) = x8 x6 x + 2.
4
2
1
Solution. f (x
MATH 103001
Winter 2013
Solution to Assignment 4
Section 3.1
For problems 9, 11, 15, nd the intervals of increase and decrease for the given function.
9. f (x) = x2 4x + 5.
Solution. f (x) = 2x 4 = 2(x 2). So f (x) < 0 on (, 2) and f (x) > 0 on
(2, +). Th
l 711 DeﬂVZ/(ﬁ/E.
12- for) ml}
The difference quotient is
f(x + h) n f (I)
h
=x/X+h—-x/A—‘
h
_\lx+h—\/;'xfx+h+\/A—'
h mlx+h+\/;
x+h—x
h
h( .¥+h+\/;)
l
_\lx+h+\/;
Then f’(x) = lim
1 l
h—-0xl.\'+h +J§ _ 2d}
The slope of the line tangent to the graph
offatx=
Answers to selected problems in 1.5
12) lim (x2 + 1)(1 2x)2 = (1)2 + 1)(1 2(1)2 = 2 32 = 18
x1
Note that the given function f (x) is a polynomial and we use the fact that
lim f (x) = f (1) = 18,
x1
i.e., we can directly evaluate the function at the given
Mathematics 103-001
Hour Test # 1
Oct. 7, 2013.
ANSWERS
(10)
(12)
(20)
x y
1. What is the slope and yintercept of the line + = 5? Rewrite the equation as
3 7
7
7
y = x + 35 and read o that m = and the yintercept is (0, 35).
3
3
x2 3
2. What is the domain
Met/KID'S Emil 2013K)
1. (6 marks) Using the deﬁnition of the derivative as a limit, ﬁnd f’(1) if ﬁx) 2 4:1:2 - 3.
E») (ii‘igmiiima rah: {NA ‘i'h‘ii‘zjﬂﬂ
( ~30 L ’
:LW ' (X-lLlLT—XZ-i'ZXL-i-LL
We L 2
:X; 54(4th + ski/(M/
W 'Jla—d—
l/\—")0
: iiwiiﬂ“: 9*) 9
Nestle and PepsiCo are the worlds largest food company and the third largest food and drink
company respectively. The food and drink industry is characterized by an organically driven
growth that comes with a necessity to change product portfolio.
It is o
UNIVERSITY OF REGINA DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 103 200710 Quiz 4 Tuesday, April 10, 2007
Time: 20 minutes Instructor: Dr. Edward Doolittle
Name: Student #:
Please do both problems 1 and 2. Each problem is worth 10 marks. You have 20 mi
UNIVERSITY OF REGINA DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 103 200710 Quiz 3 Thursday, March 22, 2007
Time: 20 minutes Instructor: Dr. Edward Doolittle
Name: Student #:
Please do both of the following problems. Each problem is worth 10 marks. You
MATH 103 200710 Quiz 2
Edward Doolittle Tuesday, March 6, 2007
Please do both of the following problems. Each problem is worth 10 marks. You have 20 minutes to nish the quiz.
1 of 2
36 1. Find the asymptotes to the function R x 4x 1, x 0. Also show that x