Deck 13: Section 8: Functions of Several Variables

Question 1

Find the point(s) on the hyperboloid where the tangent plane is perpendicular to the line with parametric equations and .

A)
B)
C)
D)
E)

Answer 1

Question 2

Find a unit normal vector to the surface at the point .

A)
B)
C)
D)
E)

Answer 2

Question 3

Find a unit normal vector to the surface at the point .

A)
B)
C)
D)
E)

Answer 3

Question 4

Find an equation of the tangent plane to the surface at the point .

A)
B)
C)
D)
E)

Question 5

Find the unit normal vector to the surface at the point .

A)
B)
C)
D)
E)

Question 6

Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the point .

A)
B)
C)
D)
E)

Question 7

Find symmetric equations of the normal line to the surface at the point .

A)
B)
C)
D)
E)

Question 8

For the function given by describe the level surface given by .

A) sphere of radius 4 centered at the origin
B) circle of radius 4 centered at the origin
C) elliptic cone centered at the origin
D) sphere of radius 16 centered at the origin
E) right circular cone centered at the origin

Question 9

Find the unit normal vector to the surface at the point .

A)
B)
C)
D)
E)

Question 10

Find a unit normal vector to the surface at the point .

A)
B)
C)
D)
E)

Question 11

Find an equation of the tangent plane to the surface at the point .

A)
B)
C)
D)
E)

Question 12

Find symmetric equations of the normal line to the surface at the point .

A)
B)
C)
D)
E)

Question 13

Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the point .

A)
B)
C)
D)
E)

Question 14

Find symmetric equations of the normal line to the surface at the point .

A)
B)
C)
D)
E)

Question 15

Find a unit normal vector to the surface at the point .

A)
B)
C)
D)
E)

Question 16

Find an equation of the tangent plane to the surface at the point .

A)
B)
C)
D)
E)

Question 17

Consider the two surfaces . Find the cosine of the angle between the gradient vectors at the point . Round your answer to one decimal place.

A) 0.5
B) 0.2
C) 0.1
D) 1.0
E) 0.0

Question 18

Identify the point(s) on the surface where the tangent plane is horizontal.

A)
B)
C)
D)
E)

Question 19

Find an equation of the tangent plane to the surface at the point .

A)
B)
C)
D)
E)

Question 20

Find the angle of inclination of the tangent plane to the surface at the point . Round your answer to two decimal places.

A)
B)
C)
D)
E)