S09mt1ansl

S09mt1ansl - (4 / 5) i + (3 / 5) k . 5: 8 6. 6: Domain is {...

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Answers for Sample First Midterm BEWARE: The following are just the numerical answers. Since the justi±cation is missing, they would not receive full credit on the real exam. 1: x 2 + y 2 + z 2 8 x +4 y 6 z +25=0. 2: c =(4 / 3) i +(16 / 3) j +(8 / 3) k and d =(2 / 3) i (1 / 3) j +(1 / 3) k . 3: 6 x + y +7 z = 31. No. 4: Unit tangent vector is (3 / 5) i +(4 / 5) k . The tangent line has equation r ( t )=(6+3 t ) i +5 j +(4+4 t ) k . The curvature is 6/125. The principal unit normal is
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Unformatted text preview: (4 / 5) i + (3 / 5) k . 5: 8 6. 6: Domain is { ( x, y, z ) | x 2 + y 2 z 2 > } . Range is R . The level set has equation x 2 + y 2 z 2 = 1 and is a hyperboloid of one sheet. 7. The limit exists and = 0. [The proof is very similar to Example 4, page 606.]...
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This note was uploaded on 09/07/2011 for the course MATH 39578 taught by Professor Penner during the Spring '09 term at USC.

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