diagram below is a contour diagram of a function T(x,y) which gives the
temperature in degrees Celsius of a metal plate at location it meters and y meters
a heater located at the origin. Use the diagram to nd the value of T(2, l). m
Include units on your
l. The wind has a velocity of i7 =10?+ 5] miles per hour and a boat is moving in the
direction 31 + 4 j . What is the component of the wind velocity in the dilution the boat
IS movmg? Give you answer as a vector in component form.
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Mac 2313 Quiz 2
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Mac 23 13 V Quiz 1
Calculus III
'1 Suppose your weight in pounds W. is a function of the number of calories C. you ca!
per day and the number of minutes I, you exercise per day. Therefore W: cfw_(C1) Is
f(C I
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01.11.2014 2:19p Sat Wk X Coll Alg Section1/11/14,
2.1
6:22 AM, 17m 52s
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College Algebra Progress Test 2 Review and Study Sheet
Communication and Vocabulary
Recognize or provide the definition of any of the following words/phrases from the lecture
notes: continuous, average rate of change, secant line, equilibrium point, root/
College Algebra Chapter 8 and 6 Test Review and Study Sheet
Communication and Vocabulary
Recognize or provide the definition of any of the following words/phrases from the lecture
notes: The Law of Exponents, an exponential function, natural logarithm, ex
Horizontal Shift
Right 2 (h=2)
Repl. x with x-h
Parent Shifted
X Y X Y
0 2 2 2
2 0 4 0
x-coord add h
y-coord no change
Vertical Shift
Up 1 (k=1)
Put +k outside
Parent Shifted
X Y X Y
0 2 0 3
2 0 2 1
x-coord no change
y-coord add k
Vertical Stretch
a=2
Mul
Name: , MAT1033C Intermediate Algebra
Unit I Sample Test
Show Your ork 9/19/2016
1. For the given equation: 2x 3y = 9, nd horizontal and vertical intercepts, slope, and graph
the equation (label intercepts). Express intercepts as orders pairs. Also, rewri
Name; LA MAT1033C Intermediate Algebra
11/17/2016 Unit III Sample Test
1. For the function f (x) = 3x2 + 6x + 5, nd the following.
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a. Vertex form of f(x) = M
b. Axis of symme
Name: Q MAT1033C Intermediate Algebra
Unit II Sample Test
Must Show Your Work for Full Credit 10/24/2016
1. State whether the equations below are quadratic by circling the correct choice.
a. 5x2+4x3=0 No
b. 3x29x4+7=0 Yes
2. Perform the indicated operatio
2.4SolvingLinearInequalities
Solve
a. 6b 10
b.
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8 g 12 3 g 2
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Solvetheinequalitynumericallyusingthecalculator
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4 x 12 5 x 4
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Solvetheinequalitygraphically.
x 3 4 x 13
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2.5AbsoluteValueEquations
andInequalities
AbsoluteValue:Theabsolutevalueof
Week 6 Handout
MAC 2311
Professor Niraj Wagh J
Section 3.3 Derivatives of Trigonometric Functions
Rule 8:
d
d
(sin x ) = cos x (cos x ) = sin x
dx
dx
d
d
( tan x ) = sec 2 x (cot x ) = csc 2 x
dx
dx
d (sec x ) = sec x tan x d ( csc x ) = csc x cot x
dx
Week 5 Handout
MAC 2311
Professor Niraj Wagh J
Sections 2.7 & 2.8 Derivatives and Rates of Change
The Legendary Derivative
(also called the Instantaneous Rate of Change of f(x) at x = a)
The derivative gives the slope of the tangent line, f(a) is the slop
Week 10 Handout
MAC 2311
Professor Niraj Wagh J
Section 4.3 Derivatives: The Shape of a Graph
Increasing/Decreasing
Increasing
A function f is said to be increasing on an interval I when, for any two numbers x1,
x2 in I, if x1 < x2, then f(x1) < f(x2).
L
Week 9 Handout
MAC 2311
Professor Niraj Wagh J
Section 3.10 Linear Approximations and Differentials
Linear Approximations
Given a function f(x), we can find its tangent at x = a. The equation of this tangent
line we will call L(x).
L(x) = f (a) + f '(a)(x
Week 7 Handout
MAC 2311
Professor Niraj Wagh J
Section 4.4 LH pitals Rule
LHpitals Rule
Suppose that f and g are differentiable and g'(x) 0 on an open interval I that
contains a (except possibly at a).
f (x)
, you get a Type I indeterminate
xa g(x)
form.
Week 3 Handout
MAC 2311
Professor Niraj Wagh J
Section 2.3 The Limit Laws (Algebraic Perspective)
The Limit Laws
Suppose that c is a constant and the limits
lim f (x)and lim g(x) exist.
xa
xa
Then,
LimitLaw1:lim [ f (x) + g(x)] = lim f (x) + lim g(x)
xa
Week 2 Handout
MAC 2311
Professor Niraj Wagh J
Section 2.1 The Tangent and Velocity Problems
Secant & Tangent Lines
A secant line is a straight line joining two points on a function.
It is EQUIVALENT to the average rate of change, or simply the slope betw
Week 1 Handout
MAC 2311
Professor Niraj Wagh J
To be successful in Calculus, you will need to have a good understanding
on BOTH Algebra and Trigonometry. For these reasons, we will spend this
first week reviewing some essential competencies of both. If yo
MAC 2311 Exam #2
Review
PROF. NIRAJ WAGH J
In addition to studying the review, you should review your notes and homework. It is not
sufficient to ONLY study the review to be fully prepared for the exam.
1. State the limit definition of the derivative.
2.
MAC 2311 Exam #1
Review
PROF. NIRAJ WAGH J
In addition to studying the review, you should review your notes and homework. It
is not sufficient to ONLY study the review to be fully prepared for the exam.
1. State the mathematical definition of the limit.
2
MAC 2311 Exam #3
Review
PROF. NIRAJ WAGH J
In addition to studying the review, you should review your notes and homework. It is not
sufficient to ONLY study the review to be fully prepared for the exam.
1. Use a linear approximation (or differentials) to
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