175 Answered Questions for the topic Calculus 3

21d

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
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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 +... more
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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 =... more
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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... more
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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.
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09/04/18

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.
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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... more
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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... more
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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.    
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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.
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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... more
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08/16/18

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!
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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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06/27/18

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) 
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04/20/18

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
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03/25/18

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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02/15/18

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
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02/13/18

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
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02/13/18

How do I do this? ------ Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 4 ln(x − y)
 Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 4 ln(x − y)
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02/05/18

i need help answering this question. find an equation of the tangent plane to the hyperboloid given by z^2 - 2x^2 - 2y^2 - 12 = 0 at the point (1,-1,4)
 and i would like steps if possible to help explain how you got the answer 
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12/23/17

Complex Analysis - Analytic Functions
Show that   f(z)=[sin(PI/z)]/(z+2)  is nowhere analytic for |z|<a , where a is a some positive number.   Can you help me to solve this problem?
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12/12/17

Use Lagrange Multipliers to solve the problem. Find the distance from the point (1,-1,2) to the plane x+y-z=3.
I do not understand the steps for the Lagrange Multipliers
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11/04/17

Evaluate the double integral D of 3/(4 +y^3) where D= {(x,y) | 0 <x <1, x^(1/2) <y <1}
Evaluate the double integral D of 3/(4 +y^3) where D= {(x,y) | 0 <x <1, x^(1/2) <y <1}
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11/04/17

What is a geometrical interpretation of a harmonic function?
More specifically, what geometrical properties does a function need to have, in order to satisfy the laplace equations? (other than it being 2nd order differentiable)
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11/03/17

Find and sketch the domain of the function
Hi, I need to know if Im right. Function is :    f(x,y)= (ln(2-x))/(1-x2 -y2 ) so x <2 and x2 +y2 <1    Graphing this, I shaded everything less than x=2 and shaded the circle. 
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