Math13S09final_sol

# Thus an equation for the tangent plane is e3 y 12z e3

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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 x-axis as the axis of symmetry. x2 − y 2 − z 2 = 0 is a cone with the x-axis as the axis of symmetry. x2 − y 2 − z 2 = 1 is a hyperboloid of two sheets with the x-axis 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.

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