Multivariable Calculus

Welcome to the "Multivariable Calculus" category on Questions LLC! Whether you're a seasoned mathematician or just beginning your journey into the realm of calculus, this category is here to provide you with a platform to ask and explore questions related to multivariable calculus. Multivariable calculus is a fascinating branch of mathematics that deals with functions of multiple variables, allowing us to analyze complex interactions and phenomena in our world. So, whether you need help solving a specific problem, understanding key concepts, or simply want to dive deeper into this intriguing subject, we're here to assist you on your quest for knowledge. Ask away and let's dive into the world of multivariable calculus together!

Questions (112)

find the volume bounded by the parabolic cylinder z=4-x^2 and the planes x=0, y=0, y=6 and z=0I just want some help figuring out
1. 3 answers
2. asked by Aryaa
3. 3,753 views
Using the Second Partials TestFind the relative extrema of f(x,y)=-x^(3)+4xy-2y^(2)+1
1. 3 answers
2. asked by tony
3. 1,365 views
Example: Suppose a consumer‘s utility function is given by U ( X ,Y ) = 𝑿^𝟒 𝒀^𝟐 . Find MRSX,Y
1. 2 answers
2. asked anonymously
3. 103 views
Evaluate the integral of (1-x) over the three dimensional cylinder x^2+y^2=1 bounded below the plane z =4+y and bounded above
1. 4 answers
2. asked by .
3. 73 views
Find the value of the double integralx*(sqrt(x^2 + y^2)) dy dx Note that the limit of x goes from 0 to 1 and the limit of y goes
1. 1 answer
2. asked by .
3. 60 views
Find the space curve, vector function r(t), where the following surfaces intersect:3x^2+y^2+1=z, x^2+3y^2+z=5
1. 4 answers
2. asked by Ken
3. 76 views
Find the directional derivative of f(x, y, z) 5y(x + z) = at P(4,1,-3)in the direction from P to Q(3,2,-2). NOTE: Enter the
1. 1 answer
2. asked by CarpoolBoi
3. 76 views
Find a vector function that represents the curve of intersection of the paraboloid z=4x2+3y2and the cylinder y=5x2 . Use the
1. 2 answers
2. asked by val
3. 58 views
Use Stokes' Theorem to evaluateC F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 9xzj +
1. 3 answers
2. asked by Taylor
3. 1,298 views
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.z = tan(u/v), u = 7s + 4t, v = 4s − 7t
1. 4 answers
2. asked by Becky
3. 2,757 views
Suppose that the height of a hill above sea level is given by z= 1000 -0.01x2 – 0.02y2. if you are at the point (60,1000) in
1. 4 answers
2. asked by Shah
3. 1,863 views
f(x, y) = 3y cos x, 0 ¡Ü x ¡Ü 2¦Ðwhat is the saddle point for this?
1. 4 answers
2. asked by sara
3. 1,216 views
find the volume of solid inside the paraboloid z=9-x^2-y^2, outside the cylinder x^2+y^2=4 and above the xy-plane1) solve using
1. 7 answers
2. asked by AIRA
3. 3,804 views
Find an equation of the tangent plane to the surface given by z = f (x,y )=𝑥^2 y + x𝑦^3 at the point (x,y)=(2,1).
1. 4 answers
2. asked by Anonymous
3. 2,812 views
Find the rate of change of f(x,y,z) = xyz in the direction normal to the surface yx^2 + xy^2 + yz^2 = 75 at (1,5,3).I keep
1. 4 answers
2. asked by .
3. 4,584 views
Evaluate the surface integralS F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
1. 4 answers
2. asked by Anon
3. 1,278 views
Find the Principal unit normal vector to the curve at the specified value of the parameter.r(t)=ti+t^(2)j+lntk, t=1
1. 4 answers
2. asked by jay
3. 1,582 views
Find the Jacobian of the transformation.x = 7v + 7w^2 y = 9w + 9u^2 z = 2u + 2v^2 ∂(x, y, z)/∂(u, v, w) ??
1. 4 answers
2. asked by durune
3. 1,417 views
find the total differential of the functionf(x,y)= xye^(x+y)
1. 4 answers
2. asked by robert
3. 1,221 views
Find the gradient of xy^2 + x^2y=4xy at the point (1,3)?
1. 4 answers
2. asked by poppy👌🤔
3. 1,036 views
Find the points of the paraboloid z=x^{2}+y^{2}-1 at which the normal line to the surface coincides with the line joining the
1. 3 answers
2. asked by RAJ
3. 524 views
Write limits of integration for the integral \int_W f(x,y,z)\,dV, where W is the quarter cylinder shown, if the length of the
1. 3 answers
2. asked by Nick
3. 1,044 views
Let S be the square in the xy-plane, oriented with the normal pointing in the positive z-direction. Estimate ∬S F⋅dS where F
1. 4 answers
2. asked by ally
3. 1,923 views
double integral of f(x,y)dxdy in polar coordinates
1. 4 answers
2. asked by Anonymous
3. 1,453 views
Use Green's Theorem to evaluateC (F · dr) (Check the orientation of the curve before applying the theorem.) F(x, y) = e^(2x) +
1. 3 answers
2. asked by Taylor
3. 635 views
The directional derivative of z = f(x,y) at (2,1) in the direction toward the point (1,3) is -2/sqrt(5), and the directional
1. 3 answers
2. asked by Dani
3. 786 views
Evaluate the double integral ∬R(3x−y)dA,where R is the region in the first quadrant enclosed by the circle x^2+y^2=4 and the
1. 3 answers
2. asked by val
3. 61 views
Use spherical coordinates.Evaluate Triple integral SSSE where E lies between the spheres x^2 + y^2 + z^2 = 25 and x^2 + y^2 +
1. 2 answers
2. asked by anon
3. 571 views
Find the volume of the solid under the plane 3x + 3y − z = 0 and above the region bounded by y = x and y = x^4
1. 3 answers
2. asked by Anon
3. 730 views
Find the volume bounded above by parabolic z = 6 - x^2 - y^2 and below by z= 2x^2 + y^2
1. 4 answers
2. asked by Lucie
3. 784 views
Set up a double integral for calculating the flux of the vector field F⃗ (r⃗ )=r⃗ , where r⃗ =⟨x,y,z⟩, through the
1. 3 answers
2. asked by A
3. 741 views
Find the total differential forf(x,y,z)= cos(4x+3y+2z+1)
1. 3 answers
2. asked by Todd
3. 372 views
find the domain of the function f (x,y) = e^-xy
1. 3 answers
2. asked by maria
3. 1,008 views
Find the area of the region bounded by the graphs x=sqrt 2sin2y ; x=0
1. 3 answers
2. asked by sedat
3. 884 views
using triple integral, find the volume of the solid bounded by the cylinder y^2+4z^2=16 and planes x=0 and x+y=4
1. 4 answers
2. asked by luthfi
3. 580 views
Consider the surface xyz = 20.A. Find the unit normal vector to the surface at the point (1, 4, 5) with positive first
1. 3 answers
2. asked by Mike
3. 978 views
find the average value of the functionf(x,y)=xe^y over the plane region R is the triangle with vertices (0,0), (1,0) and (1,1)
1. 4 answers
2. asked by Anonymous
3. 1,015 views
Find equations of the tangent plane and normal line to the surface x=4y2+1z2−342at the point (-9, -9, 3). Tangent Plane: (make
1. 2 answers
2. asked by val
3. 66 views
Suppose that f(x,y,z)=x2yz−xyz3is a function of three variables. 1. Find the gradient of f(x,y,z). Answer: ∇f(x,y,z)= 2.
1. 2 answers
2. asked by val
3. 51 views
Find the directional derivative of f(x,y,z)=z3−x2yat the point (-2, 5, 1) in the direction of the vector
1. 2 answers
2. asked by val
3. 47 views
For the following pair of functions f and g, determine if the level curves of the functions cross at right angles, and find
1. 1 answer
2. asked by Ms Sue
3. 62 views
Hello, I have to find the volume of the region enclosed by the paraboloid z=(x^2)+(y^2) and the planes z=1 and z=3 , so well i
1. 1 answer
2. asked by Alice
3. 457 views
Hello, I have the next exercise about chain rule in multivariable calculus:I have to show that the differential equation:
1. 2 answers
2. asked by Susan
3. 668 views
Let S be the funnel shaped surface defined by x^2 + y^2 = z^2 for 0<z<9(a) Sketch S (b) Determine the outward pointing normal to
1. 3 answers
2. asked by Ariana
3. 372 views
Find critical points forf(x,y)= x^3+y^3-15x^2-6xy+18y^2+39x+138y I know you first take the partial derivative of x and y, but I
1. 2 answers
2. asked by Erica
3. 540 views
Evaluate the surface integralS F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
1. 1 answer
2. asked by Anon
3. 751 views
Evaluate the surface integralS F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
1. 1 answer
2. asked by Anon
3. 845 views
Use Stokes' Theorem to evaluateC F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj +
1. 1 answer
2. asked by Anon
3. 612 views
Use a triple integral to find the volume of the given solid.The tetrahedron enclosed by the coordinate planes and the plane 8x +
1. 2 answers
2. asked by Anon
3. 525 views
Find the mass and center of mass of the solid E with the given density function ρ.E is bounded by the parabolic cylinder z = 1
1. 2 answers
2. asked by Anon
3. 571 views

Multivariable Calculus

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