Newest Calculus 3 Questions | Wyzant Ask An Expert

08/26/17

Calculus III Question

A weight of 100 pounds is suspended by two ropes A and B. Rope A makes an angle of 30 degrees with the ceiling and rope B makes an angle of 45 degrees with the ceiling. What are the magnitudes of... more

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Calculus 3

05/24/17

a) eliminate the parameter t b) write the equation in scalar nonparametric form and c) express dy/dx and d^2y/dx^2 as functions of t

x=4(sin^2)tcost y=4sin(cos^2)t

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Calculus 3 Calculus Vector Calculus

03/30/17

Lagrange Multipliers

Find all of the extrema of g(x,y,z)=xyz on the surface z=e^(-x^2-y^2).

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Calculus 3

03/28/17

Identify the quadric surface: -4x^2+y^2-4z^2=4

How would I trace this on the xy and yz coordinate plane as as well as the planes y=±4

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Calculus 3 Math Calculus Vector Calculus

03/15/17

Use differentials to approximate

Use differentials to find the approximate amount of copper used in the four sides and bottom of a rectangular copper tank that is 6 feet long, 4 feet wide and 3 feet deep inside if the sheet of... more

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Calculus 3 Math Calculus Vector Calculus

03/12/17

Vector Fields

For each vector field in R4 given below, either find a function for which it is the gradient, or explain why no such function exists. Variables are in the order x, y, z, w. a.(siny + wcosx + 1)e1 +... more

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Calculus 3 Math Calculus

03/11/17

Vector Fields

Let F(x,y)=3x^2yi+(x^3+y^3)j. By integrating, find a function f so that F=del f. Don't forget your constants of integration!

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Calculus 3 Math Calculus

03/11/17

Vector Fields

Show that the path x(t)=(cos(t-1),t^3-1,1/t-2) is tangent to the surface x^3+y^3+z^3-xyz=0 when t=1

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Calculus 3 Math Calculus

02/18/17

Partial Derivatives

Let g(x,y)=(xy)^(1/3). e.Does the graph of g have a tangent plane at (0,0)? Explain briefly. f.Is g differentiable at (0,0)? Explain briefly. I asked this question yesterday but was still... more

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Calculus 3 Math Calculus

02/17/17

Partial derivatives (multiple parts)

Let g(x,y)=(xy)^(1/3). a. Is g continuous at (0,0)? I put down yes since it's not undefined there. b.Calculate ∂g/∂x and ∂g/∂y when xy≠0. This wasn't too bad and pretty straightforward. I... more

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Calculus 3 Math Calculus

02/17/17

Gradients of a function

Here's the question: Find the most general function f:R^2 --> R such that ∇f(p)=p for each p∈R^2. So, I'm guessing this means that I just need to find a function of x and y such that the... more

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Calculus 3 Calculus

02/17/17

Is this function differentiable?

Is f(x,y)=sqrt(x^2+y^2) differentiable at (0,0)? Justify. I don't think the partial derivatives exist due to the limit definition, so can I say that the function isn't differentiable? Or is... more

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Calculus 3

02/15/17

For the plane curve r(t)=ti+(lncost)j+0k Determine T(t):

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Calculus 3

01/23/17

Length is independent of parametrization

Length is independent of parametrization: To illustrate that the length of a smooth space curve does not depend on the parametrization you use to compute it, calculate the length of one turn of the... more

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Calculus 3 Integral

11/15/16

I=R⌠⌠⌠f(x,y,z)dv

Set up an iterated integral to evaluate I=R⌠⌠⌠f(x,y,z) dv, where R is the region in the first octant bounded by the surface z=x+y^2, the cylinders y=2sqrt(x), x=2sqrt(y), and the... more

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Calculus 3 Calculus

11/15/16

f(t)=1/T⌠1/t (1/x)ln(tx) dx

If f(t)= ⌠1/t (1/x)ln(tx) dx 1/T⌡ where T is a constant with the same physical dimensions at t, find f'(t). Try to write the answer in a form which... more

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Calculus 3 Calculus Multivariable Calculus

11/07/16

The parabolas y=x^2, y=x^2+1, y=(x-2)^2, y=(x-2)^2+1

The parabolas y=x^2, y=x^2+1, y=(x-2)^2, y=(x-2)^2+1 Intersectto form a curvilinear quadrilateral R. The change of variable u=y-x^2, v=y-(x-2)^2 map R onto a square in the uv-plane. Use the... more

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Calculus 3 Sequences Series

11/04/16

PLEASE HELP with SEQUENCES!! Determine whether the sequence is increasing, decreasing, or not monotonic.

Determine whether the sequence is increasing, decreasing, or not monotonic. an = 4n(−7)n Is the sequence bounded? Yes or No? Explain.

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Calculus 3 Sequences Series

11/04/16

Determine whether the sequence is increasing, decreasing, or not monotonic.

Determine whether the sequence is increasing, decreasing, or not monotonic. an = 1/(6n+7) Is the sequence bounded? Yes or No? Explain.

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Calculus 3 Optimization

11/03/16

maximum and minimum values of the function f(x,y,z)=x + 2y subject to the constraints y^2 + z^2 = 289 and x + y + z = 5

I know how to solve these problems with two constraints, but this one quickly falls apart and becomes realistically "unsolvable." I'm trying to find the max and the min and at what points they... more

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Calculus 3 Calculus 2

10/27/16

The position function of a particle is given by r(t) = <t^2, 9t, t^2 - 16t> When is the speed a minimum?

The position function of a particle is given by r(t) = <t^2, 9t, t^2 − 16t> When is the speed a minimum?

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Calculus 3 Polar Coordinates Calculus 2

10/22/16

Polar Coordinates DIFFICULT question! PLEASE HELP!!!

When recording live performances, sound engineers often use a microphone with a cardioid pickup pattern because it suppresses noise from the audience. Suppose the microphone is placed 4 m from the... more

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Calculus 3 Polar Coordinates Calculus 2

10/21/16

Find the area of the region that lies inside both curves. PLEASE HELP!

Find the area of the region that lies inside both curves.r = √3 cos θ, r = sin θ Thank you in advance!

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Calculus 3 Polar Coordinates Calculus 2

10/21/16

Find the area of the region that lies inside the first curve and outside the second curve.

Find the area of the region that lies inside the first curve and outside the second curve.r = 9 cos θ, r = 4 + cos θ Please show steps! Thanks in advance!

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Calculus 3 Area Polar Coordinates Calculus 2

10/20/16

Find the area of the shaded region r=v? PLEASE HELP!

Find the area of the shaded region r=√θ (r is equal to the square root of theta) I can't show the picture but the shaded region is in the fourth quadrant. Thanks in advance!

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Calculus III Question

a) eliminate the parameter t b) write the equation in scalar nonparametric form and c) express dy/dx and d^2y/dx^2 as functions of t

Lagrange Multipliers

Identify the quadric surface: -4x^2+y^2-4z^2=4

Use differentials to approximate

Vector Fields

Vector Fields

Vector Fields

Partial Derivatives

Partial derivatives (multiple parts)

Gradients of a function

Is this function differentiable?

For the plane curve r(t)=ti+(lncost)j+0k Determine T(t):

Length is independent of parametrization

I=R⌠⌠⌠f(x,y,z)dv

f(t)=1/T⌠1/t (1/x)ln(tx) dx

The parabolas y=x^2, y=x^2+1, y=(x-2)^2, y=(x-2)^2+1

PLEASE HELP with SEQUENCES!! Determine whether the sequence is increasing, decreasing, or not monotonic.

Determine whether the sequence is increasing, decreasing, or not monotonic.

maximum and minimum values of the function f(x,y,z)=x + 2y subject to the constraints y^2 + z^2 = 289 and x + y + z = 5

The position function of a particle is given by r(t) = <t^2, 9t, t^2 - 16t> When is the speed a minimum?

Polar Coordinates DIFFICULT question! PLEASE HELP!!!

Find the area of the region that lies inside both curves. PLEASE HELP!

Find the area of the region that lies inside the first curve and outside the second curve.

Find the area of the shaded region r=v? PLEASE HELP!

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