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Math 2224 Multivariable CalculusSam El}: Triple Integrals in Cylindrical and Spherical
Coordinates
|. Integration in Cylindrical Coordinates
Cylindrical Coordinates are obtained by combining polar coordinates in the xyplane with the
usual z-axis.
A
Defini
STJCIaSS Time or CRN 5 '- '39?) - t-I.
_.-"'./READ THE DIRECTIONS. YOU MUST SHOW ALL WORK ON THIS TEST AND USE METHODS LEARNED IN
_»
CLASS OR FROM THE WORKSHEETS TO RECEIVE FULL CREDIT. CALCULATORS ARE PERMITTED. 100 pt.
total
1. Differentiate the follow
1. [20 points, 10 points each] What is your best estimate of the mean and standard
deviation of the test scores for the entire population, based on the sample data.
OK, this one Should have been easy!
2 = (;)(663 + 629 + + 706)
1
7 5850
9)( )
= 650
S; = (
Hyperbolic Trigonometric Functions
Just as trigonometry can be performed on the unit circle, it can also be performed on the unit hyperbola:
x2 y2 : 1.
Dene the hyperbolic cosine mctiorr by
cosh(x) :
and the hyperbolic sine function by
I ex 7 gear
smh(x)
1. Which of the following is the inverse of the function f(_;1:7) : 22: + 3'?
a) flmi) = 21? 7 3
b) 1619:) = 72177 3
. 1,7 _$_3
, 2
d) f1(m):;+3
2. Find
_ m2+2178
A=111n
mrwgBmIQ
and
_ 10:35 + 7:153 +1?
B i 5175 + 817 7 172 '
a) A does not exist, B = 0