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32 Answered Questions for the topic Multivariable Calculus

Multivariable Calculus Math Integral Calculus

09/17/20

Evaluate the line integral with respect to arc length.3 variables

Evaluate the line integral with respect to arc length where C is given by ∫c x ds x = t, y = t sin t, z = t cos t, 0 ≤ t ≤ √(2)firstly subbed t into equation as x=tthen differentiated x, y and... more
Multivariable Calculus Directional Derivatives

05/29/20

Please help with this problem.

You are to design a stainless-steel fermenter, which has a right circular cylindrical shape with a height of 1.2 m and radius of 0.3 m. How fast will the fermenter’s volume change with a small... more
Multivariable Calculus Calculus

03/24/20

Multivariable Calculus Question - Global max & min

Find the global maximum and minimum to the function f (x,y,z) = xy2z3 on the set S = (x, y, z) : x2 + y2 + z2 ≤ 1 .
Multivariable Calculus Calculus Vector Calculus

01/11/20

Projectile Motion using Vector Calculus

Trebuchet can throw an 80 lb rock up to 100 yards. The maximum height that the rock reaches as it flies through the air toward a fortress wall 100 yards away is 20 yards, calculate the initial... more
Multivariable Calculus Gradient Tangent

01/03/20

Find the plane which is tangent to a surface at a point.

Multivariable Calculus Math Calculus

06/01/19

Multivariable Calculus Problem

Please help me with the problem below, I am really stuck:In 2-space, find the unit vectors orthogonal to y = e ^ 2x at x = 0.
Multivariable Calculus Gre Reference Request

04/04/19

Math GRE: Calculus Textbooks - is Spivak + Stewart + Rudin sufficient?

Recently, I splurged and spent $1000 in math textbooks in preparation for the Mathematics GRE subject test. So far, in terms of calculus books, I have purchased Spivak, Stewart, and Baby Rudin.... more
Multivariable Calculus Calculus Gre

03/24/19

GRE Mathematics Multivariable Calculus?

I'm studying for the GRE subject test on 4/5, and I've been going through the princeton review book, which seems to be the canonical guide. In the multivariable section the theorems are pretty... more
Multivariable Calculus Calculus Real Analysis

03/22/19

Geometrical Interpretation of Cauchy Riemann equations?

Differentiation has an obvious geometric interpretation, and the Cauchy Riemann equations are closely linked with differentiation. Do the Cauchy Riemann equations have a geometric interpretation?
Multivariable Calculus Linear Algebra

03/18/19

Divergence as transpose of gradient?

In his online lectures on Computational Science, Prof. Gilbert Strang often interprets divergence as the "transpose" of the gradient, for example [here](http://youtu.be/gYME3EbIqV4?t=31m50s) (at... more
Multivariable Calculus Calculus Optimization

03/15/19

How to know whether Lagrange multipliers gives maximum or minimum?

My book tells me that of the solutions to the Lagrange system, the smallest is the minimum of the function given the constraint and the largest is the maximum given that one actually exists. But... more
Multivariable Calculus Calculus Optimization

03/14/19

Why does a distance and its square reach their minimum at the same point?

There is a question in my calculus textbook that asks to find a point on the parabola $y^2 = 2x$ that is closest to point $(1,4)$. They want us to first use the distance formula, but then... more
Multivariable Calculus

06/26/17

Find the minimum distance from the origin to the surface

Find the minimum distance from the origin to the surface z2 = (x-1)2+(y-1)2   
Multivariable Calculus Calculus Linear Functions

04/13/17

Find a linear function whose graph is the plane that intersects the xy-plane along the line y= x+7 and contains the point (-4,-4,-21).

Find a linear function whose graph is the plane that intersects the xy-plane along the line y= x+7 and contains the point (-4,-4,-21).
Multivariable Calculus

03/03/17

Find the maximum value of f(x,y) = x^2y^7 for x,y ≥ 0 on the unit circle

Find the maximum value of f(x,y) = x2y7 for x,y ≥ 0 on the unit circle
Multivariable Calculus Limits Critical Point

12/28/16

Finding critical points and limits.

Let f(x,y) = 1/(x2 - y) (a) Determine the critical points of f.(b) Does the limit of the function f at the point (0, 0) exist? Justify your answer
Multivariable Calculus Calculus Plane

12/06/16

use cylindrical coordinates to evaluate the triple integral that gives the mass the solid

use cylindrical coordinates to evaluate the triple integral that gives the mass the solid lying under the cone z=10-√(x2+y2), and above the xy-plane, if the density p is given by p(x,y,z)=x2+y2+z2.... more
Multivariable Calculus Calculus Calculus 3

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
Multivariable Calculus Domain And Range Domain

10/23/16

Finding Domain and Range of a Multivariable Function

for the following function find the domain D and range T and show that for every c ∈ T there exists x,y such that f(x,y) = c. Sketch the Domain. The following is my own answer but I am unsure if... more
Multivariable Calculus Equation Calculus 3

09/14/16

equation of plane

find equation of a plane that contains the line x=3t y=2+t z=-2t and parallel to the intersection of planes 2x-y=0 and y+z=-1 i dont know what to cross im so confused please help
Multivariable Calculus Calculus 3

08/26/16

find equation of line through the point (1,-1,1) perpendicular to the line 3x=2y=z and parallel to plane x+y-z=0

i have no idea solving the problem :((
Multivariable Calculus Calculus 3

08/25/16

equation of plane that contains point (2,0,3) and line x=-1+t, y=t, z=-4+2t

I tried solving it and I got -x-5y+3z=7 but it seems wrong. Any help please?
Multivariable Calculus

12/01/15

which of the following is divisible by all of the integers from 1 to 10 inclusive? A)23*34 B)34* 45 C) 45*56 D) 56*67 E)67*78

This is a hard question whaich found in UKMT question test online
Multivariable Calculus Parametric Equations Calculus 3

11/15/15

Evaluate the following integral using any Vector Calculus method

Evaluate the following integral using any Vector Calculus methodThe integral with bounds C; [(4+eyz)i+(xzeyz+2yz)j+(6z2+xyeyz+y2)k] dot dr, where C is the part of a curve on x5+y3z=25 from (1,2,3)... more
Multivariable Calculus

08/13/15

The vector from the point (1,2, -3) to the centre of the sphere x2+y2+z2-kx+3y-lz = 1 is given by < 3, h, -2 > . Then the value of hkl is?

The vector from the point (1,2, -3) to the centre of the sphere x2+y2+z2-kx+3y-lz=1  is given by < 3, h, -2 > . Then the value of hkl is?
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