Name _
Multivariable Calculus
Date _
Problem Set #15
Please show all work to each of the following problems.
r
r
x
x
1. Determine whether or not the vector field F ( x, y ) = ( ye + sin y ) i + ( e +
Name _
Date _
Multivariable Calculus
Problem Set #2
1. What type of conic section is described by the equation 2 y 2 3x 2 4 y + 12 x + 8 = 0 ? If it is
an ellipse, find the vertices and foci. If it is
Name _
Multivariable Calculus
Date _
Problem Set #4
For the test on Sections 12.5-12.7, you should be able to, using appropriate diagrams, explain
how the conversion formulas between cylindrical and r
Name _
Multivariable Calculus
Date _
Problem Set #3
Please show all work to each of the following questions.
1. Consider the set of all points P such that the distance from P to A ( 1,5,3) is twice th
Name _
Multivariable Calculus
Date _
Problem Set #5
For the assessment on Sections 13.1-13.3, you should be able to prove the following statement:
r
r
r
If r ( t ) = c , where c is a constant, then r
Name _
Multivariable Calculus
Date _
Problem Set #6
1. Find the torsion of each of the following curves:
r
3
a) r ( t ) = t , 2t ,3t for arbitrary time t .
r
b) r ( t ) = sinh t , cosh t , t at the po
Name _
Multivariable Calculus
Date _
Homework Set #8
Please show all work to each of the following questions.
1. Compute lim
( x + h ) ln ( ( x + h )
2
)
+ y 2 x ln ( x 2 + y 2 )
h
h 0
.
2. The wave h
Name _
Multivariable Calculus
Date _
Problem Set #7
Please show all work to each of the following problems.
2
2
2
1. Let g ( x, y , z ) = ln ( 25 x y z ) .
a) Evaluate g ( 2, 2, 4 ) .
b) Find the doma
Name _
Multivariable Calculus
Date _
Problem Set #10
Please show all work to each of the following problems.
3
2
2
2
1. Consider the function f ( x, y ) = 2 x + xy + 5 x + y . Find the local maximum a
Name _
Multivariable Calculus
Date _
Problem Set #9
Please show work to all of the following questions.
1. Four positive numbers, each less than or equal to 50, are rounded to the first decimal place
Name _
Multivariable Calculus
Date _
Problem Set #11
Please show all work to each of the following problems.
1. Compute
8
2
2. Compute
1 x 2 y 2 dA , where D is the disk x 2 + y 2 1 . Hint: Before doi
Name _
Multivariable Calculus
Date _
Problem Set #14
Please show all work to each of the following problems.
y
1. Compute the gradient vector field for the function f ( x, y, z ) = x cos .
z
2. Creat
Name _
Multivariable Calculus
Date _
Problem Set #13
Please show all work to each of the following problems.
1. Evaluate the triple integral
x dV , where E
E
is the bounded by the paraboloid
x = 4 y
Name _
Multivariable Calculus
Date _
Problem Set #12
1. Find the volume of the solid that lies inside the sphere x 2 + y 2 + z 2 = 16 and outside the
cylinder x 2 + y 2 = 4 .
2. Use polar coordinates
Name _
Date _
Multivariable Calculus
Problem Set #1
Please show all work to each of the following questions, including steps to
any integrals that may need to be calculated.
1. Find the area A of the