S05mt1ansl - j(4 4 t k The curvature is 6/125 The principal...

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MATH 226 CALCULUS III Prof Baxendale 2/11/05 Answers for Sample First Midterm BEWARE: The following are just the numerical answers. Since the justification 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
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Unformatted text preview: j + (4 + 4 t ) k . The curvature is 6/125. The principal unit normal is-(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 941.]...
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