Math 1320 Lab 11 Name: _
L3 1. Determine Whether each of the following equations is a solution of Laplaces equation
um + aw; = 0:
(a) u = 3:2 + y2
VII 2
11?
US$23
2 ,2/0 I ,4 ,51711 4 Salim. (g 2. An ideal gas satises the relation PV 2 nRT, where P is pre
Math 1320
Practice Exam 2
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1. Suppose a function f (x) has a fourth derivative f (4) (x) that takes on values between 3
and 2 in the interval (0, 2). Suppose w(x) is the cubi
Math 1320-4 Midterm Exam 2
March 29 2013
Name and uID:
Write your answer in the space provided. Show work for full credit.
No textbook, formula sheet, notes, calculator, computer or other mobile device allowed.
This exam is individual.
This exam consists
Math 1320
Exam 1
Total 7 problems and 85/80 points (number of points is subject to change).
1. Consider the solid obtained from a hemisphere with radius r that has a hole of radius a
drilled through its center.
(a) (5 points) Sketch a cross-section of the
Math 1320
Pop Quiz 1 (W13)
Name and uID:
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1. Find the equation of the tangent plane to f (x, y) = 2x2 + y 2 at the point P0 (1, 1, 3).
Solution: We have fx (x, y) = 4x so fx (1, 1) = 4 and
Math 1320
Pop Quiz 2 (W14)
Name and uID:
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1. Find the equation of the tangent plane to the surface x2 + xy + z 2 = 1 at the point
P0 (1, 1, 1).
Solution: Let F (x, y, z) = x2 + xy + z 2 .
Math 1320
Pop Quiz 3 (W15)
Name and uID:
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1. Consider the function f (x, y) = 2x2 y 2 . Find the directional derivative of f (x, y) at
the point (1, 1) in the direction 3i + 2j. hint: The
Math 1320
Week 8 Quiz
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1. Consider the two vectors
a = 3, 1, 2 and b = 2, 2, 2 .
(a) Compute a b.
(b) Are a and b orthogonal?
Solution: We have:
a b = 3, 1, 2 2, 2, 2
= (3)(2
Math 1320
Week 7 Quiz
Name and uID:
Write your answer in the space provided. Show work for full credit.
1. Consider the function
f (x) =
1
.
(2 x)3
(a) Use the binomial series to expand f (x) as power series in x. What is its radius of
convergence?
For fu
Math 1320
Week 7 Quiz Retake
Name and uID:
Write your answer in the space provided. Show work for full credit.
1. (a) (4 points) Write the function f (x) =
1
as a power series in x.
1x
(No justication needed).
(b) (4 points) Use the series in part (a) to
Math 1320-1
Week 10 quiz
Name and uID:
Write your answer in the space provided. Show work for full credit.
1. (a) Transform the equation of the surface z = r2 from cylindrical to Cartesian coordinates.
Solution: z = x2 + y 2 .
(b) Identify this surface.
S
Math 1320
Week 12 quiz
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1. Consider the function f (x, y) = cos 1 + x y.
(a) What is the domain of f ?
Solution: We need the square root to be well dened:
D = cfw_(x, y) | 1
Math 1320
Super Quiz 1 (Week 4)
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1. (10 points) (a) Sketch the region bounded by y = 1 x2 and the y = 0 axis.
Solution: [ sketch ]
(b) Find the volume of the solid obtained b
Math 1320
Super Quiz 2 (Week 9)
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1
1. (10 points) Find the Taylor polynomial of degree 3 of the function f (x) =
about
x
a = 1.
Solution: Calculate the derivatives and evalua
Math 1320
Quiz W13
Name and uID:
Write your answer in the space provided. Show work for full credit.
1. Find an equation for the plane tangent to the surface z = xy 2 + xy at the point (2, 1, 4).
Solution:
z
z
= y2 + y
= 2.
x
x (x,y)=(2,1)
z
z
= 2yx + x
Math 1320
Practice Exam 1
1. Find the volume of the solid obtained by rotating the region bounded by the following
curve about the line x = 2. Sketch the region, the solid, and a typical disk or washer.
y = x, y = x.
Solution: Here the cylindrical shell m
Math 1320
Practice Final Exam
Name and uID:
Write your answer in the space provided. Show work for full credit.
1. Stretched 4 feet beyond its natural length, a certain spring exerts a restoring force of
200 N. What work must we do to stretch the spring 1
Math 1320
Week 10 Lab
Name and Unid: :
1. Describe the sphere given by the equation x2 + y 2 + z 2 = z, i.e. state is its radius and
at which point is it centered (hint: complete the square).
Solution:
Write the equation as x2 + y 2 + (z 1/2)2 = 1/4 to se
/0
% Code by
% Problem 1 Revised
clc, clear all, close all
Ts= . l: .1: 6.4;
x=cos(Ts.*2.*pi);
fourier= fft(x);
fourier=fourier.*1/64; % this normalizes the funciotn
b=fftshift(fourier);
c=abs(b);
figure(l)
plot(linspace(-10/2,10/2-10/64,64),c)
% Problem
Name
Student ID 7%
Math 1320
Spring 2014
SAMPLE EXAM II
This is only to give you a general idea of What to expect. The actual exam
may or may not include problems similar to those given here, and it may be
longer or shorter.
Instructions: Show all of
N ame
Student ID #
Math 1320
Spring 2014
SAMPLE EXAM I
This is only to give you a. general idea of what to expect. The actual exam
may or may not. include problems similar to those given here, and it may be
longer or shorter.
Instructions: Show all of
Math 1320
February 14, 2014
EXAM 1
Instructions: Show all of your work for full credit. (20 1,)oints) 1. Find the volume of the solid obtained by rotating the region bounded
by the curves :1: = y3/2, 5r: 2 1, x = 2, about the yaxis.
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Math 1320
March 28, 2014
EXAM II
Instructions: Show all of year work for full credit.
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