190 Answered Questions for the topic Calculus 3

Calculus 3 Algebra 2

03/22/22

#### Show that (0, 0) is the only critical point of f(x,y)=(xy)/(x^2+y^2+1)

I know that to find the critical point, you take the partial derivatives with respect to x and y and find the values of x and y when the partial derivatives are equal to zero. I set the partial...
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02/22/21

#### How to solve these computations

Hey I'm looking to check my answers to make sure these computations are correct. The definition used isLet u = i + 2j - k, v = 3i - j + 4k and w = 2j - kCalculate u • vCalculate u x vCalculate (u x...
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#### How to find the plane to the surface with parametric equations below?

Find the tangent plane to the surface with parametric equations x(u,v)=u2+2u, y(u,v)=3v-2u, z(u,v)=6v-10 at point (8,14,2).

#### Compute the volume in the first octant

Use a double integral to compute the volume in the first octant above the region in the xy plane bounded by y=1-x2 , y=0, and x=0; and between the planes z=2-y and z=1

11/11/20

#### How to find double integral with change of variables

I am trying to complete a double integral with change of variables, and am not sure where I am going wrong (somewhere in setting up the integral is my guess). Thank you for any help you can...
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#### Finding the equation of a circle with a curvature equal to the curvature of a given curve at a point

"Find an equation for the circle of curvature of the curve r(t)=8t i + sin(5t) j at the point (4pi,1). (the curve parameterizes the graph of y=sin(5/8X) in the xy plane) Ive already found v(t)=8...
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11/17/19

#### Use the change of variable formula evaluate the double integral ∫ ∫R 1/ (√1-x^2-y^2) dA where the region R is the part of the cartesian plane above the xaxis between the circles x^2+y^2=1 & x^2+y^2=4

Can you please draw the region as well so that I can get more clarification

09/25/19

#### Stokes' Theorem and Cylindrical Coordinates

For a function B=z i − 3x j + 2z k prove the Stokes’ theorem over the circle x2+y2=1 acting as a base of the upside-down paraboloid z = 1 − x2 − y2, z ≥ 0.Hint: convert this function...
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04/19/19

#### Calculus 3 - Newton Raphson Method

Hi there. Please help me solve this problem. I don't even know where to start. Thanks much.Use the Newton-Raphson Method to show that xn+1 = 2xn3 + xn2 + 10 numerator (3xn2 +...
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10/07/18

#### Matrices question. PLSSSSS HELP.

4. Let n≥2, let A and B b en×n matrices and let On be the n×n matrix with every entry 0.(b) Suppose that A2 = On. Show that In − A is invertible, and that (In − A)-1 = In + A.(c) Suppose that Am =...
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09/05/18

#### Suppose U = <2,3,4> Then:

<4,5,3> makes a (right, obtuse, or acute) with u.
<5,-1,2> makes a (right, obtuse, or acute) with u.
<-8,0,4> makes a (right, obtuse, or acute) with u.
<3,2,-3> makes a...
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09/04/18

#### Let V = <1, 3, 3>. Find a unit vector for this.

I have 1/sqrt(10), 3/(sqrt(10)), 3/sqrt(10). I cannot understand why this is not the answer. It is pointing in the same direction.

#### C-(-4,2,4). Find the distance between the point (x,y,z) and C.

I had tried the points (0,0,0)-(-4,2,4) and then use the distance formula, but that has not worked. Then I tried (1,1,1), but that also did not work. I am lost. Any help is needed.

Calculus 3 Vectors

08/31/18

#### Find the length of ->OR.

(We are talking about vectors.
R = (4, 5, 5).
Then it has,
||->OR|| = _____.
I'm not sure how you find OR if you do not have what O is. Thank you. (Arrows are supposed to be on...
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Calculus 3

08/30/18

#### Needing to find the X(t) and Y(t) in the equation. This involves Calculus and the hint was Recall the parametric representation of the unit circle as (cost,sin

While a planet P rotates in a circle about its sun, a moon M rotates in a circle about the planet, and both motions are counterclockwise in the same plane. Let's call the distance between M and P...
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Calculus 3 Vectors

08/29/18

#### Find the equation of a sphere if one of it's diameters has endpoints (-10,0,-6) and (4, 14, 8).

I have written:
(x+3)2+(y-7)2+(z-1)2-sqrt(588)/2 = 0.
But it is marked incorrect.

Calculus 3 Vectors

08/29/18

#### Find an equation of the largest sphere with center (5, 3, 6) and is contained in the first octant. Be sure your formula is monic.

I had put the equation as:
(x-5)^2+(y-3)^2+(z+6)^2
However it was viewed as incorrect. Also they had that it equaled zero.
equation input = zero.

Calculus 3

08/19/18

#### Find the equation of the sphere centered at (−1,10,2) ( − 1 , 10 , 2 ) with radius 4.

Find the equation of the sphere centered at (−1,10,2) ( − 1 , 10 , 2 ) with radius 4.
___________________ = 0
Give an equation which describes the intersection of this sphere with the plane...
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#### Double integral - calculating area

Calculate the area of the region bounded by the two curves, y = 4 - x2 and y = x + 2.
The answer is meant to be 9/2 but I just cannot get it!!! Maybe my bounds are incorrect.... help!

07/07/18

#### Find an area bounded by a graph

I need help with this task.
cx(x^2/a^2+y^2/b^2)=y^2,x=b^2/c

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