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Multivariable Calculus > Final > Flashcards

Final Flashcards

1
Q

Find the equation of a line given: 2 points

A
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2
Q

Find the equation of a line given: 1 point and 1 vector

A
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3
Q

Find the equation of a line given: 1 point and 1 perpendicular plane

A
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4
Q

Find the equation of a line given: 1 point and 1 perpendicular line

A
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5
Q

Find the equation of a line given: 2 intersecting planes

A
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6
Q

Find the equation of a plane given: 1 point and 1 normal vector

A
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7
Q

Find the equation of a plane given: 1 point and 1 line

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8
Q

Find the equation of a plane given: 3 points

A
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9
Q

Find the equation of a plane given: 2 lines

A
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10
Q

Find the equation of a plane given: a tangent plane

A
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11
Q

Find the equation of a plane given: 1 line and 1 perpendicular plane

A
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12
Q

(Line Testing) Parallel Line

A
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13
Q

(Line Testing) Intersecting Line and Perpendicular Line

A
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14
Q

(Line Testing) Skew Line

A

not parallel or intersecting

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15
Q

Distance Equation

A
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16
Q

Directional Derivative

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17
Q

Direction of the Maximum Rate of Change

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18
Q

Maximum Rate of Change

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19
Q

Tangent Plane Equation/Linear Approximation

A
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20
Q

Prove a limit does NOT exist

A
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21
Q

Prove a limit DOES exist

A
  • can be continuous and have a constant denominator
  • can simplify to get something to get a non-undetermined limit
  • can apply the squeeze theorem
22
Q

Find and Classify local extrema

A
23
Q

Find global extrema

A
24
Q

Lagrange Multipliers

A
25
Q

What do double integrals find?

A

Volume

26
Q

Polar Coordinates (2D)

A

*Add an extra r

27
Q

What do triple integrals find?

A

Mass or Density

28
Q

Cylindrical Coordinates (3D)

A

*Add an extra r

29
Q

Spherical Coordinates (3D)

A

*Add an extra

30
Q

Scalar Line Integrals

A
31
Q

Change of Coordinates

A

(1) graph the given bounds and find the equation for each line segment
(2) put these equations equal to u and v
(3) solve for x and y to find the Jacobian

(4) solve using

32
Q

Change Order of Integration

A

(1) sketch the given integrals
(2) reverse the order in which the figure is being cut
(3) keep what is inside of the integrand the same

33
Q

Vector Line Integrals

A
34
Q

Fundamental Theory of Line Integrals Criteria (Line Integrals)

A

F is conservative, C is not closed, and the Potential Function can be found

35
Q

Potential Function

A
36
Q

Fundamental Theory of Line Integrals Formula (Line Integrals)

A
37
Q

What is the line integral if F is conservative and C is closed

A

equals 0

38
Q

Green’s Theorem Criteria (Line Integrals)

A

F is not conservative, C is closed, has continuous partials, and positively oriented (if not add a - in front)

39
Q

Green’s Theorem Formula (Line Integrals)

A
40
Q

curl F

A

Tells how rotational something is

41
Q

div F

A

Tells how much an object expands/contracts under the velocity field

42
Q

Parametric Surfaces

A

(1) draw the function given
(2) put in terms of r(u,v) and assign u and v

43
Q

Tangent Plane to S (Parametric Surfaces)

A
44
Q

Surface Integrals

A
45
Q

area(S)

A
46
Q

Flux

A

How much coffee is made per second

47
Q

Stokes Theorem Criteria (Surface Integrals)

A

F is a curl field, S is closed, and you can find G such that

48
Q

Stokes Theorem Formula (Surface Integrals)

A
49
Q

What is the surface integral if F is a curl field and S is closed?

A

equals 0

50
Q

Divergence Theorem Criteria (Surface Integrals)

A
51
Q

Divergence Theorem Formula (Surface Integrals)

A

Multivariable Calculus (1 decks)

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