(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

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
Transcribed Image Text:(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
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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

Calculus homework question answer, step 1, image 1

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

Similarly to find the z intercepts we substitute x = 0

Calculus homework question answer, step 1, image 2

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

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