Which two go with change of variable integration?

Jacobian, Determinate of a partial matrix

Which concept goes with the area between two curves (non-rectangular)?

Dbl. integral with variable and constant bounds, argument 1.

A useful trigger for changing the order of integration may be (select all that apply)...

When I am in need of a term for u-substitution, When I am "simple" in the latter term of integration

Composed of partial derivatives

Which technique best describes finding a projection of one vector onto another?

Dot them, divide by a magnitude, and multiply by a u.

Parametric equations are..

Equations that relate to another variable

What is the second derivative test?

A technique for categorizing extrema

Which technique allows you to calculate the area between two curves.

Integral bounds from inner function to outer function

How do you find dx/dy in terms of t?

Divide the derivatives of x and y with respect to 't'.

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Calculus 3 Review

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A #math #Quiz about calculus 3 topics

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Questions 26

Answers

1
Which two go with change of variable integration?
Polar
Jacobian
Determinate of a partial matrix
Gradients
2
What is the appropriate conversion for polar coordinates?
y2 = x2 = r
y = sqrt(r2-4)
x = y cos (t)
cos-1(x) = sin-1(y)
3
Which concept goes with the area between two curves (non-rectangular)?
Single integral with variable bounds, argument 1.
Dbl. integral with variable and constant bounds, argument 1.
Triple integral with variable bounds and variable argument.
Double integral with constant bounds and argument 1.
4
Which of the following is the equation for a parabola?
x2=t, y = t
y = t, x = t
x = t, y = sqrt(t)
x = t, y = t2 (t >0)
5
Limits are
What I "approach"
Something my Grandmother makes for dinner
The "smallest" minima
The extrema values
6
Volume of F(x,y) = sqrt(X^2+y^2) would be best integrated with...
Rectangular
Cylindrical
Polar
Spherical
7
The argument in a triple integral can be thought of as a function in _____ space.
4D
1D
2D
3D
8
Directional derivative can be calculated from...
Cross products and partials
Gradients and maxima
Gradients and dot products
Partials and parametrics
9
A useful trigger for changing the order of integration may be (select all that apply)...
When I am in need of a term for u-substitution
When I have a square-root in the function
Whenever I am integrating in polar or cylindrical bounds.
When I am "simple" in the latter term of integration
10
Gradient is...
A level curve
Centered at the origin
A negative magnitude
Composed of partial derivatives
11
A double integral with constant bounds has a region that is
rectangular
spherical
circular
a prism
12
Dot product can be written using
cross product
cosine
sine
absolute values
13
Which two conic section has only one focus?
Ellipse
Hyperbola
Parabola
Circle
14
Which technique best describes finding a projection of one vector onto another?
Cross the two vectors and divide by the unit vector
Dot the two vectors and divide by a magnitude
Dot them, divide by a magnitude, and multiply by a u.
Cross the two vectors
15
Which operation yields a magnitude proportional to the parallelogram created by vectors?
Direct Product
Orthogonal Product
Dot Product
Cross Product
16
Gradient equal to 0 implies
Maxima
Minima
Sale point
Critical point
17
Parametric equations are..
Any equation dealing with temperature
Equations that equal each other
A pair of measurements
Equations that relate to another variable
18
What is the second derivative test?
A way of locating extrema
A technique for categorizing extrema
D= fxx*fyy + (fxy)^2
A technique for determining concavity
19
Which technique allows you to calculate the area between two curves.
Integral bounds from outer function to inner function.
Integral bounds from left function to right function.
Integral bounds from inner function to outer function
Constant bounds representing the minimum and maximum values.
20
A unit tangent vector is found using...
Partial derivatives
Dot product
Gradient
Derivative
21
What rule allows us to multiply itterated integrals?
Bezout's Lemma
Fundamental Theorem of Calculus
Cole's Law
Gauss' Law
22
Lagrange multipliers...
Scale parallel vectors
Determine relative extrema
Describe parallel scalars
Determine absolute extrema
23
Which is used for calculating a projection of one vector onto another?
Dot Product
Geometric Product
Scalar Product
Cross Product
24
Arc length can be best related to...
Vectors
Extrema
Pythagorean theorem
Cross products
25
How do you find dx/dy in terms of t?
Divide the derivatives of x and y with respect to 't'.
Take partials of x, y and multiply them
Multiply the derivatives of x and y with respect to t.
Take x,y partials and divide them
26
The limit of x/x is...
0
1
X/X

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