Problem

Sketch the indicated curves and surfaces. An elec…

Problem 40 Easy Difficulty

Sketch the indicated curves and surfaces.
At a point $(x, y)$ in the $x y$ -plane, the electric potential $V$ (in volts) is given by $V=y^{2}-x^{2} .$ Draw the lines of equal potential for $V=-9,0,9$

Answer

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Calculus 3

Basic Technical Mathematics with Calculus

Chapter 29

Partial Derivatives and Double Integrals

Section 2

Curves and Surfaces in Three Dimensions

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Video Transcript

based on the scenario presented in the problem, were asked to sketch the echo potential curves at the was 2.1 points around 0.5. You know that to do this we well, first that our equation called to a constant in this case will call it g being able to be. And here is we saw this. We can see the, uh, okay spirit of 16 plus X squared plus y squared is equal. Teoh 8/3. Well, we can say that. Ah, ex query plus y squared is equal 64 elite squared minus 16. So this equation will basically give us the different level curves based on our valuable The So went these records 2.0, we end up with an equation Ex cleared. That's why it's clearing is equal to zero. But that implies that we have the circle of radius zero, which is really just a point of origin. Green equals 1.0. We have an equation. Ex clear. That's why squared is equal to 48. So our radius, this would be a circle with the radio Bert affiliate or or heard of three and a re equals zero plea fire you have division explained was Y squared equals 112 which implies a circle with a radius. Ah, four squared seven. So if you put all of these, then the the echo potential curves at the given values of being would look like the graph that I have provided here.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Problem

Sketch the indicated curves and surfaces. An elec…

Problem 40 Easy Difficulty

Sketch the indicated curves and surfaces.
At a point $(x, y)$ in the $x y$ -plane, the electric potential $V$ (in volts) is given by $V=y^{2}-x^{2} .$ Draw the lines of equal potential for $V=-9,0,9$

Answer

Related Courses

Basic Technical Mathematics with Calculus

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Discussion

Top Calculus 3 Educators

Catherine R.

Anna Marie V.

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Caleb E.

Calculus 3 Courses

Vectors Intro

Vector Basics - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 29

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Caleb E.

Vectors Intro

Vector Basics - Example 1

Basic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Caleb E.

Vectors Intro

Vector Basics - Example 1

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Anna Marie V.

Kayleah T.

Caleb E.

Vectors Intro

Vector Basics - Example 1

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus