chapter 12

Question 1

cylinder

Answer 1

consists of all lines paralell and passing through a given curve
for the equation one of the variables will not be squared. the plane is defined by the others

Question 2

ellipsoid

Answer 2

x^2+y^2+z^2=1

can be over different radius’

Question 3

equation of a cone

Answer 3

x^2+y^2=z^2

the one on the other side is the axis it is on

Question 4

cylinder

Answer 4

x^2 + y^2 = r^2

Question 5

hyperboloid

Answer 5

x^2+y^2-z^2=1

Question 6

hyperboloid of 2 sheets

Answer 6

-x^2-y^2+z^2=1

Question 7

eliptic paraboloid

Answer 7

x^2 + y^2 = z

Question 8

x^2 + y^2 = z

Answer 8

eliptic paraboloid

center axis is z

Question 9

-x^2-y^2+z^2=1

Answer 9

hyperboloid of 2 sheets

Question 10

x^2+y^2-z^2=1

Answer 10

hyperboloid

Question 11

x^2 + y^2 = r^2

Answer 11

cylinder

Question 12

x^2+y^2=z^2

the one on the other side is the axis it is on

Answer 12

equation of a cone

Question 13

x^2 - y^2 = z

Answer 13

hyperbolic paraboloid

Question 14

hyperbolic paraboloid

Answer 14

x^2 - y^2 = z

Question 15

domain with 2 variable

Answer 15

find both variables such that they satisfy the equation

Question 16

how to find all the level curves equation

Answer 16

set the equation equal to c

Question 17

given graph of contour lines

find a linear equation

Answer 17

1. find change in z/x
2. find change in z/y
3. use same point
   z-z1=(x-x1)dx+(y-y1)dy

Question 18

steps for partial derivative

Answer 18

1. find your main equation and partiallly derive it for each of the variables in it.
2. derive each of the other equations such that they give you what they want.
3. use sum of products to sum them and cancel to the derivative you desire