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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.2: Ellipses

Problem 63E

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Question

4 5 6

Directions: Solve the following problems NEATLY, COMPLETELY and CORRECTLY. You
must submit the problem set through Canvas in PDF file. Do NOT use graphing devices in your
work.
1.
Identify the surfaces of the following equations by converting them into
equations in the Cartesian form. Show your complete solutions.
(a) ² = 4 + 4²
(b) p = sin sine
2.
Evaluate the double integral that will find the volume of a solid bounded by
1-2y²-3² and the zy- plane.
(Hint: Use trigonometric substitution to evaluate the formulated double integral.)
3.
Set-up the iterated double integral in polar coordinates that gives the volume
of the solid enclosed by the hyperboloid = = √√1+ + and under the plane z = 5.
4.
Evaluate the double integral:
So de dy.
(Hint: Change the order of integration to dy dr.)
5.
Use Cartesian coordinates to evaluate
JJ v av
dV
where D is the tetrahedron in the first octant bounded by the coordinate planes and the
plane 2x + 3y +z = 6. Use dV= dz dy dr. Draw the solid D.
6.
Set up the triple integral that will give the following:
(a) the volume of R using cylindrical coordinates with dV = r dz dr de where R:0≤
2≤ 1,0 ≤ y ≤ √1-2², 0≤ ≤ √√4-(2²+ y²). Draw the solid R.
(b) the volume of the solid B that lies above the cone z = √√/32² + 3y² and below the
sphere a² + y² +2²= z using spherical coordinates. Draw the solid B

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