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185 Answered Questions for the topic Calculus 3

Calculus 3 Calculus Circle


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... more


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
Calculus 3 Calculus Matrices


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
Calculus 3 Vector Obtuse Triangle


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
Calculus 3 Vector Unit Vector


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.
Calculus 3 Distance Vectors


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


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
Calculus 3


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
Calculus 3 Vectors


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


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


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
Calculus 3 Calculus Integrals


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!
Calculus 3 Calculus Calculus 2


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  
Calculus 3 Square Root Volume


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) 
Calculus 3


Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=5x+y on the ellipse x^2+36y^2=1.

 Use Lagrange multipliers to find the maximum and minimum values
Calculus 3


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
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