2. Answer the following for the function f (x, y) = 3+ x² + ya. Graph at least 3 level curves for the function. Be sure to label the curves withtheir z-values.b. Graph the function in R³.

Name: 2. Answer the following for the function f (x, y) = 3+ x² + ya. Graph
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Description: 2. Answer the following for the function f (x, y) = 3+ x² + ya. Graph at least 3 level curves for the function. Be sure to label the curves withtheir z-values.b. Graph the function in R³.

Answered: 2. Answer the following for the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Answer the following for the function f (x, y) = 3+ x² + y
a. Graph at least 3 level curves for the function. Be sure to label the curves with
their z-values.
b. Graph the function in R³.

Expert Solution

Step 1

(a) The level curves are the projection of surface z = f(x,y)=c on xy-plane.

For $f (x, y) = 3 + x^{2} + y$

$3 + x^{2} + y = c x^{2} + y = c - 3$

i) For $c = 3$

$x^{2} + y = 0 y = - x^{2}$

This is a parabola open downwards.

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