Assignment 24

course MTH 272

......!!!!!!!!...................................Applied Calculus II

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Asst # 24

07-06-2006

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16:26:55

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**** Query problem 7.2.52 (was 7.2.48) identify quadric surface z^2 = x^2 + y^2/4.

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16:30:32

z^2 = x^2 + y^2/4

sqrt (z^2) = sqrt (x^2) + sqrt (y^2 / 4)

z = x + y/2

This fits the equation for an elliptic paraboloid: z= x^2 / a^2 + y^2 / b^2

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16:30:33

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**** What is the name of this quadric surface, and why?

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16:31:35

The name of this quadric surface is an elliptic paraboloid because the xy-trace is an ellipse, while the xz and yz-planes are parabolas.

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16:31:36

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**** Give the equation of the xz trace of this surface and describe its shape, including a justification for your answer.

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16:35:30

Set y=0

z^2 = x^2 + (y^2)/4

z^2 = x^2 + 0/4

z^2 = x^2 +0

z^2 = x^2

This is a parabola because it contains a squared term.

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16:35:31

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**** Describe in detail the z = 2 trace of this surface.

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16:39:34

2^2 = x^2 + (y^2)/4

4 = x^2 + (y^2)/4

I'm not really sure what to do from here. Maybe you could take the square root of both sides, leaving you with:

sqrt(4) = sqrt(x^2) + sqrt(y^2 /4)

but then that leaves you with all of the terms being either positive or negative

+,- 2 = +,- x + +,- (y/2)

I don't think this is the right answer, so maybe you don't take the square root, and it leaves you with:

2^2 = (x-0)^2 + (y/2 - 0)^2, which would be an ellipse with a center of (0,0) and a radius of 2.

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16:39:37

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Please notify your instructor of the error, using the Submit Work form, and be sure to include the date 07-07-2006.

This looks good. Let me know if you have questions.