182 Answered Questions for the topic Calculus 3


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... more


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 +... more


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 =... more


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... more


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.


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... more


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... more


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.    


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.


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... more


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!


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  


Find the volume of the solid

Find the volume of the solid bounded by the plane z = 5 and the hyperboloid z = SquareRoot(9+x^2+y^2) 


Calculating work done by force field ( multivariable calculus )

Calculate the work done by the force field F(x,y,z)=(xx +z2 )i + (yy  + x2 )j + (zz +y2)k when a particle moves under its influence around the edge of the part of the sphere x2 +y2 +z2 =4 that lies... more


Differential Equation Question

How would I write this in matrix form (x' = AX)    x' = x y' = y   Note: Is it supposed to be like this: x' = (1 v 1)(x v y) or x' = (1 + 0 v 1 + 0)(x v y)? Note: the "v" means the value after... more


Find Z(subx) and z(suby)

Let exyz = 2. Find zx and zy in 3 ways and check for agreement.    a. use result of a previous exercise (i.e. Assume that F(x,y,z(x,y))=0 implicitly defines z as a differentiable function of x... more


How do I do this? Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x2 + 4xy + y2 − 34x − 32y + 38

Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously.f(x, y) = x2 + 4xy + y2 − 34x − 32y + 38
1 3 4 5 6 7 8

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