194 Answered Questions for the topic Calculus 3

Calculus 3 Calculus Calculus 2

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  
Calculus 3 Square Root Volume

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) 
Calculus 3

06/25/18

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

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

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
Calculus 3

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
Calculus 3

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
Calculus 3

02/13/18

How do I do this? For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = 36 x + 6 y + xy

For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously.f(x, y) = 36x + 6y + xy
Calculus 3

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)
Calculus 3

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 

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?
Calculus 3

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
Calculus 3

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}
Calculus 3

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)
Calculus 3

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. 

11/02/17

Consider the curve C given by the equation

Consider the curve C given by the equation: C · · · √ x + √ y = √ a, where a is a constant, a > 0. Let (x0, y0) with x0 > 0, y0 > 0, be a point on C. If (x1, 0) and (0, y1) are x and y... more
Calculus 3 Calculus

10/25/17

triple intergral

Evaluatethe triple integral of x^2 where D is the region inside the cylinder x^2+y^2=9 which is bounded below by the plane z=0 and bounded above by the plane 4x+4y+z=19I know the limits of the z... more
Calculus 3 Calculus Calculus 2

10/25/17

Given any Cartesian coordinates, (x,y), there are polar coodinates

Given any Cartesian coordinates, (x,y), there are polar coordinates (r,θ) with (-pie/2) < θ ≤ (pie/2). Find polar coordinates with (-pie/2) < θ ≤ (pie/2) for the following Cartesian... more
Calculus 3 Math Vectors Projections

10/10/17

Vector Projection, and Orthogonal Complement

I have projections down good, but I keep getting the orthogonal complement wrong.    QUESTION   a = <0,2,-5>     b = <6,8,-3>   compute the projection of a onto b and the vector... more
Calculus 3 Calculus 2

10/09/17

Use substitution x=sin theta to evaluate integrate x^2/(1-x^2)^5/2

Full working out please
Calculus 3

09/26/17

Use the Chain Rule to find dz/dt. z = xy^9 − x^2y, x = t^2 + 1, y = t^2 − 1

 just a regular calc 3 question using chain rule. not sure what im doing wrong
Calculus 3

09/18/17

Where L intercepts P

let P be the plane in R3 given by x + 2y + z = 0. Let L be the line through two points (1,0,1) and (0,1,1). Give the coordinates of the point where L intercepts P.   

09/11/17

Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1>

Find two unit vectors orthogonal to a = <4,-1, 2> and b = <3, 3, 1>   First vector = <?, ?, ?> Second vector = <?, ?, ?>

09/11/17

Find the velocity, acceleration, and speed of a particle with position function

Find the velocity, acceleration, and speed of a particle with position function r(t) = <-7tsin(t), -7tcos(t), 4t^2>   v(t) = <?, ?, ?> a(t) = <?, ?, ?> |v(t)|= ?
Calculus 3 Calculus

09/11/17

Checking Over a Calculus 3 Problem

A plane Q is defined by the equation 4(x-8)+3(y-7)-5(z+2)=0.   Give the most obvious example a point P lying on the plane Q.   I believe this to be (8,7,-2)    Then the next part asks for the... more

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