(4) Sketch the surfaces. Show some work including intercepts.(a) z² + 2? = 4(d) + y² + z² = 1(b) z = r² + y?(e) z = V9 – r² – y²(c) z = Vr2 + y?(f) z = -V4 - x² – y2

Answered: (4) Sketch the surfaces. Show some work…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(4) Sketch the surfaces. Show some work including intercepts.
(a) z² + 2? = 4
(d) + y² + z² = 1
(b) z = r² + y?
(e) z = V9 – r² – y²
(c) z = Vr2 + y?
(f) z = -V4 - x² – y2

Expert Solution

Step 1

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

The function x² + z² = 4 is the equation of cylinder. The radius of the cylinder is 2.

To find x-intercepts, we substitute z = 0

Therefore, we get

So the x-intercepts are (2, 0, 0) and (-2, 0, 0).

Similarly to find the z intercepts we substitute x = 0

So the z-intercepts are (0, 0, -2) and (0, 0, -2).

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