40 Answered Questions for the topic Multivariable Calculus

Multivariable Calculus

11/08/21

#### Letf=x2 +y2(1+x)3 (a) Show that f has only one critical point and that it is a local minimum at that critical point. (b) Show that f has no minimum value.

Let f = x^2 +y^2 (1+x)^3(a) Show that f has only one critical point and that it is a local minimum at that critical point.(b) Show that f has no minimum value.
Multivariable Calculus

10/25/21

(a) Show that the minimum of x+y+z subject to xyz = 1,x ≥ 0,y ≥ 0,z ≥ 0is3. Be sure to show why the minimum exists. Suggestion: Use the gradients to find the critical point, on the constraint... more
Multivariable Calculus

10/25/21

#### (a) For a constant a, find the average y value for the region between y = a + 1 and y = x2 + a. (b) For what value of a is the average y value in Part (a) zero?

(a) For a constant a, find the average y value for the region between y = a + 1 and y = x^2 + a.(b) For what value of a is the average y value in Part (a) zero?
Multivariable Calculus Calculus

09/14/21

#### Find the length of the shortest curve between (1, 0, 0) and (1, 1, 1) on the surface x2 + y2 = z2 + 1. Be sure to explain why your answer is correct.

Find the length of the shortest curve between (1, 0, 0) and (1, 1, 1) on the surface x2 + y2 = z2 + 1. Be sure to explain why your answer is correct.
Multivariable Calculus Calculus

09/14/21

#### Consider the dashed line through the (0,0,0) and (0,1,1), and the dotted line through (0, 1, 0) and (1, 0, 0) as in the figure.

Consider the dashed line through the (0,0,0) and (0,1,1), and the dotted line through (0, 1, 0) and (1, 0, 0) as in the figure.(a) Let f(t) be the point that moves along the dashed line, with... more
Multivariable Calculus Math Calculus Mathematics

01/03/21

#### Approximating a multivariable plane using a set of single variable equations

I am attempting to make a multivariable equation that describes pump flow when 2 different characteristics are manipulated. My equations are:y = 8.1429x + 0.0057 when z=10y = 7.3571x + 0.0043 when... more

#### How to find double integral with change of variables

I am trying to complete a double integral with change of variables, and am not sure where I am going wrong (somewhere in setting up the integral is my guess). Thank you for any help you can... more
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

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

01/03/20

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

Multivariable Calculus Math Calculus Algebra

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 Gre Exam

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 Gre Exam

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 Complex 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 Lagrange Multiplier

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

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 Limits Of A Function

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

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