quiz04' - x = y = 0, and the limit of the given function is...

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Quiz 4 Solutions 1. Find the unit tangent vector T ( t ) to the curve r ( t ) = (sin t ) i + 4 j - (tan t ) k at t = π 4 . The tangent vector is r 0 ( t ) = (cos t ) i - ( 1 cos 2 t ) k . At t = π 4 , r 0 ( π 4 ) = 2 2 i - 2 k . So, ± ± r 0 ( π 4 ± = q 1 2 + 4 = 3 2 . Thus, T ( π 4 ) = r 0 ( π 4 ) | r 0 ( π 4 ) | = 1 3 i - 2 2 3 k . 2. Find the limit, if it exists, or show that the limit does not exist: lim ( x,y,z ) (0 , 0 , 0) xy + yz + zx x 2 + y 2 + z 2 Suppose we approach the origin along the positive z -axis. Then
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Unformatted text preview: x = y = 0, and the limit of the given function is 0. Then suppose we approach along the line in the xz-plane where x = z . Then y = 0, and the given function simplies to x 2 2 x 2 , which approaches 1 2 as x goes to 0. Since 0 6 = 1 2 , the limit does not exist. 1...
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