SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 1
MATH 150 - D200 Fall 2012
Instructor: Allan Majdanac
October 1, 2012, 8:30 9:20 a.m.
Name:
(please print)
family name
given name
student number
SFU-email
SFU ID:
@sfu.ca
Signature:
Instructions:
MATH 150 - Practice for Midterm 2
1. The graph of a function is given. At what numbers is the function not dierentiable? Explain why.
2. Using the denition of the derivative, evaluate g (x) if the function is given by g (x) =
x2 9
.
x2
3. Dierentiate the
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12.0rthogonal Trajectories. Z
(a) TWO curves are called orthogonal if at each point of interse tion their
tangent lines are perpendicular. l
Recall: The 0G2: M
(b) Two families of curves are orthogonal trajectories of each oth
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A Rational Parameterization of the Unit Circle
The diagram below illustrates how _ through the
point (-1,0) _ the circle in _ one
point, if we imagine the _ varying from
_ to _:
Let us find a description of these _:
Each line goes through the point _ and
1
Solving the DE
dy
= ky : To help your understanding of solving
dt
differential equations (DEs), I am reminding you how we solve other equations:
Suppose we want to find out which y makes the following linear equation true:
Equation (1): a= y + b
You pro
31
11. Example. At what point on the curve 3; = e is the tangent line parallel
to the line y = 2:13? +WQ Fug: CM Januam :
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J 3.2 The Product and Quotient Rules
1. Quote. Fiv
$ 4.1 Maximum and Minimum Values
"6/ . Quote. I feel the need of attaining the maximum of intensity with the
0. minimum of means. It is this which has led me to give my painting a
character of even greater bareness.
a?"
9 (Joan Miro, Catalan-Spanish artis
Hi
1
9. Closed Interval Method. To find the absolute maximum and mini-
mum values of a continuous function f on a closed interval [(1, b]:
(a) Find the values of f at the critical numbers of f in (1,1).
(b) Find the values of f at the endpoints of the int
( 6. Must Know! > 1
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Optimization
Some guidelines in solving optimization problem:
Read the problem at least _ and underline
pertinent information.
Sketch a _ of the problem if applicable.
Use a _ statement to introduce variables.
Find an _ that relates the variables of y
1
Failure of Newton-Raphson method:
1. Newton-Raphson method stops if f ( xn ) 0 . If
that happens try a _ initial guess. However,
it can happen that f and f have the _ root.
2. Newton-Raphson method does not always
converge. No amount of _ will bring us
2.5 Continuity
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2.5 Continuity (Homework)
Current Score : / 23
1 of 7
Deva Gara
MATH150 D100 Calculus I, section D100, Fall 2016
Instructor: Petra Menz
Due : Tuesday, September 27 201
2.7 Derivatives and Rates of Change
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2.7 Derivatives and Rates of Change (Homework)
Current Score : / 13
Deva Gara
MATH150 D100 Calculus I, section D100, Fall 2016
Instructor: Petra M
2.1 The Tangent and Velocity Problems
WebAssign
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Deva Gara
MATH150 D100 Calculus I, section D100, Fall 2016
Instructor: Petra Menz
Due : Tuesday, September 27 2016 08:00 PM PDT
2.1 The Tangent
3.1 Derivatives of Polynomials and Exp. Functions
WebAssign
3.1 Derivatives of Polynomials and Exp. Functions (Homework)
Current Score : / 13
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Deva Gara
MATH150 D100 Calculus I, section D100, F
2.3 Calculating Limits Using the Limit Laws
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2.3 Calculating Limits Using the Limit Laws (Homework)
Current Score : / 19
Deva Gara
MATH150 D100 Calculus I, section D100, Fall 2016
Ins
2.2 The Limit of a Function
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2.2 The Limit of a Function (Homework)
Current Score : / 19
1 of 8
Deva Gara
MATH150 D100 Calculus I, section D100, Fall 2016
Instructor: Petra Menz
Due :
3.2 The Product and Quotient Rules
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3.2 The Product and Quotient Rules (Homework)
Current Score : / 12
Deva Gara
MATH150 D100 Calculus I, section D100, Fall 2016
Instructor: Petra Men
4. A rocket is launched vertically and is tracked by a radar station located
on the ground 5 km from the launch pad. Suppose that the elevation
angle 9 of the line of sight to the rocket is increasing at 3 per second
when 9 = 60. What is the velocity of t
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3.11 Hyperbolic Functions
1. Quote. You could rewrite it in terms of hyperbolic functions, but I
dont know if itd be easier.
(Posted by Dave at. 3.08. Mathematics CyberBozud, 11!;Lp: / /www.sosnmth.c01u,
MATH 150 Quiz 1
Solution
Wednesday January 13
1. Let f be the function.
(a) Since f is odd we have f (x) = f (x). Thus for any (x, y) on the graph, the
point (x, y) is also on the graph. Hence, (5, 3) is on the graph of f .
(b) Since f is odd we have f (x
2.2 The Limit of a Function
1. Quote. Black holes are where God divided by zero.
Steven Wright, American comedian, 1955x2 x 2
2. Problem. Let f (x) =
.
x2
(a) Determine the domain of f . Sketch it.
(b) Complete the table
x
f (x)
1
1.9
1.99
1.999
1.9999
x
Preamble
Each group member should read through this entire document. It provides an overview of the group
project that you will complete in your design labs. It also gives rubrics for how you will be assessed. I will
provide more detail throughout th
SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 1
MATH 150 - D100 Spring 2017
Instructor: Jens Bauch
January 31, 2017, 8:30 - 9:20 am
(please print)
Name:
family name
given name
@sfu.ca
SFU ID:
student number
SFU-email
Signature:
Instructions:
1
Math 151 Midterm 2 Practice Questions
1. Compute the following derivatives. You do not need to simplify your
answers.
(a) f(:L') if fa) = (23:6 43: + art.
3
M): Hub-Loam (ms-*4)
sec 9:
mam '
(b) 9%?) if W?) =
(arm 3 an"\(gecx+aexx) cfw_sawdfex t Hf]
._.