4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as surface function in the form f(1, y). (b) Describe and draw the shape of the surface function using contour lines and algebraic analysis as needed. Explain the contour shapes in all three orthogonal directions and explain and label all intercepts as needed. (c) Consider the contour of the surface function on the plane z = 0. Write the general equation for this contour in vector form.

4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as surface function in the form f(1, y). (b) Describe and draw the shape of the surface function using contour lines and algebraic analysis as needed. Explain the contour shapes in all three orthogonal directions and explain and label all intercepts as needed. (c) Consider the contour of the surface function on the plane z = 0. Write the general equation for this contour in vector form.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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