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Chapter 12: Q11E (page 734)

Question:

Short Answer

Expert verified

Use the Geogebra or the same graphic tool to plot the surface.

Step by step solution

01

Using the Geogebra,

Using Geogebra we plot the surface. The image is given below.

02

Step 2:

Use the Geogebra or the same graphic tool to plot the surface.

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Most popular questions from this chapter

Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point.

a.\(\left( {{\rm{4,\pi /3, - 2}}} \right)\)

b.\(\left( {{\rm{2, - \pi /2,1}}} \right)\)

Use polar coordinates to find the volume of the given solid.

Under the cone \({\rm{z = }}\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} {\rm{ }}\)and above the disk\({{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ }} \le {\rm{ 4}}\)

Use cylindrical coordinates Evaluate\(\iiint_{\text{E}}{\sqrt{{{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}}}\text{dV}\), where \({\rm{E}}\) is the region that lies inside the cylinder \({{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ = 16}}\) and between the planes \({\rm{z = - 5}}\) ,\({\rm{z = 4}}\).

Calculate the integrated integral \(\int\limits_{ - 3}^3 {\int\limits_0^{\pi /2} {(y + {y^2}\cos x)dxdy} } \)

a) In what way Fubini and Clairault’s theorem are similar?

b) If \(f(x,y)\) is continuous on \(R = (a,b) \times (c,d)\) and \(g(x,y) = \int\limits_0^1 {\int\limits_0^1 {f(s,t)dtds} } \) for \(a < x < b\), \(c < y < d\), Show that \({g_{xy}} = {g_{yx}} = f(x,y)\).
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