Let f .x; y; z/ D .x2 C z2/sin xy 2 C yz2. Let P0 be the poi
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Let f .x; y; z/ D .x2 C z2/sin xy 2 C yz2. Let P0 be the point .1; 1; ?1/. (a) Find the gradient of f at P0. (b) Find th
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Let f .x; y; z/ D .x2 C z2/sin xy 2 C yz2. Let P0 be the point .1; 1; ?1/. (a) Find the gradient of f at P0. (b) Find the linearization L.x; y; z/ of f at P0. (c) Find an equation for the tangent plane at P0 to the level surface of f through P0. (d) If a bird flies through P0 with speed 5, heading directly toward the point .2; ?1; 1/, what is the rate of change of f as seen by the bird as it passes through P0? (e) In what direction from P0 should the bird fly at speed 5 to experience the greatest rate of increase of f ?
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