Math 2110Q, Section 17, Exam #1
This exam consists of ten problems, each weighted equally. Justify your responses and Show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Academic Code is mandatory
13.6 Cylinders and Quadric Surfaces
Cylinders Graphs in xyzspace whose equation is f (x, y) = C, f (y, z) = C or f (x, z) = C.
(Remark)
f (x, y) = C
f (x, y) = C
draws a curve in R2
draws a surface in R3
Example Sketch x2 + y 2 = 1 in R2 and in R3 respec
Multivariate Calculus; Fall 2013
3.6
S. Jamshidi
Cylinders and Quadric Surfaces
Objectives
I know the definition of a cylinder.
I can name the 6 quadric surfaces, write their equation, and sketch their graph.
Lets take stock in the types of equations we
Sketching Surfaces in 3d
In practice students taking multivariable calculus regularly have great difficulting visualising
surfaces in three dimensions, despite the fact that we all live in three dimensions. In these
notes well develope some technique to h
Section 11.4: Equations of Lines and Planes
Definition: The line containing the point (x0 , y0 , z0 ) and parallel to the vector ~v = hA, B, Ci
has parametric equations
x = x0 + At,
y = y0 + Bt,
z = z0 + Ct,
where t R is a parameter. These equations can b
Math 2110Q
Final Review
Name:
April 28, 2014
1. Given the points P (2, 0, 6) and Q(2, 8, 5)
(a) Find the poosition vector equal to P Q .
(b) Find 2 vectors with length 2 parallel to P Q .
(c) Find the vector-valued function r(t) of the line segment P Q.
2
Math 2110Q
Exam 1 Review
Name:
February 21, 2014
1. Given the points P (2, 0, 6) and Q(2, 8, 5)
(a) Find the poosition vector equal to P Q.
(b) Find 2 vectors with length 2 parallel to P Q.
(c) Find the vector-valued function r(t) of the line segment P Q.
Math 2110Q
Exam 2 Review
Name:
April 3, 2014
1. Find fx and fy for the following functions
(a) f (x, y) = cos(xy)
(b) f (x, y) = xy
(c) f (x, y) = x ln(x2 + y 2 )
2. Find fx , fy and fz for f (x, y, z) = cos(x + y + z)
3. For
f (x) =
xy
+ y2
0
x2
if (x, y
14.4: Tangent Planes and Linear
Approximation
Anthony Rizzie
University of Connecticut
Fall 2016
learning objectives
After today, you should be able to:
1. Understand the concept of a tangent plane and how it
relates to a surface
2. Compute an equation fo
12.5 Equations of Lines and Planes
Anthony Rizzie
University of Connecticut
Fall 2016
learning objectives
After today, you should be able to:
1. Understand the definition and different forms of a line in R3
2. Know what it means for lines to be intersecti
Math 2110Q, Section 06, Exam #2
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Student Code is mandator
Math 2110Q, Section 17, Exam #2
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Academic Code is mandato
Math 2110Q, Section 06, Exam #1
This exam Consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own7 and compliance with the
UConn Student Code is mandator
4 law:
I- 'VCator Equation 0F a Lin: 75
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jive: Hat PoSHIoh VCOJ'OI F 0F a faint on a Line
2' Para rad-er equqhms cfw_907 q line '1,th ru'unt; (Kg, 74v)
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Math 2110Q, Section 17, Exam #2
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Academic Code is mandato
Math 2110Q, Section 014, Exam #1
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Student Code is mandato
Math 2110Q, Section 06, Exam #1
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Student Code is mandator
Math 2110Q, Section 17, Exam #1
This exam consists of ten problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Academic Code is mandatory
Math 2110Q, Section 06, Exam #2
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Student Code is mandator
Math 2110Q, Section 002, Exam #1
This exam consists of eight problems, each weighted equally. Justify your responses and show all
work, unless indicated otherwise. All work submitted is to be your own, and compliance with the
UConn Student Code is mandato
14.1 Functions of Several Variables
14.3 Partial Derivatives
Anthony Rizzie
University of Connecticut
Fall 2016
learning objectives
After today, you should be able to:
1. Understand the definition of a function in two or more
variables and its domain
2. K
14.6: Directional Derivatives and the
Gradient Vector
Anthony Rizzie
University of Connecticut
Fall 2016
learning objectives
After today, you should be able to:
1. Understand the concept of a directional derivative
2. Compute directional derivatives and f
14.7: Maximum and Minimum Values
Anthony Rizzie
University of Connecticut
Fall 2016
learning objectives
After today, you should be able to:
1. Understand the difference between a local max, local min,
and saddle point
2. Find all critical points for a giv