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Unformatted text preview: gt;
y
is normal to the surface and tangent plane. Thus an equation for the tangent plane is
e3 y + 12z = e3 + 24.
3. x2 − y 2 − z 2 = −1 is a hyperboloid of one sheet with the xaxis as the axis of symmetry.
x2 − y 2 − z 2 = 0 is a cone with the xaxis as the axis of symmetry.
x2 − y 2 − z 2 = 1 is a hyperboloid of two sheets with the xaxis as the axis of symmetry.
z z y x
x y
x2 − y 2 − z 2 = −1
z x y
x2 − y 2 − z 2 = 1
1 x2 − y 2 − z 2 = 0 4. For double integrals we think of the integrating the height of boxes over a region in the plane.
In this case, the height is given by z = 1 + x2 + y...
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This note was uploaded on 01/20/2014 for the course MATH 13 taught by Professor Weiss during the Spring '07 term at Tufts.
 Spring '07
 Weiss
 Math, Calculus

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