30 Answered Questions for the topic Multivariable 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.

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....
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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...
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03/24/19

#### 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?

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?

03/22/19

#### 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...
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03/21/19

#### 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

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...
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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

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...
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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

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).

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

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

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....
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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...
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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...
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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

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 :((

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?

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

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)...
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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?

07/20/15

#### Area of a parallelogram using 4 points

I need some help using vectors to find the area of this parallelogram. I use three points to create two vectors with the same initial points and use a 2x2 determinant to compute the cross...
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04/27/15

#### Suppose S_1={u_1,u_2} and S_2={v_1,v_2} are each independent sets of vectors in an n-dimensional vector space V.

Let us assume that every vector in S_2 is a linear combination of vectors in S_1.Question: Does that mean that S_1 and S_2 are bases for the same subspace of V?I know that the answer to this...
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