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Unformatted text preview: ∂x ∂t = 4 cos 4 t and ∂y ∂t = 6 cos 6 t . ±or the other two quantities in (1), we use the implicit function rule. ∂z ∂x =∂F ∂x ∂F ∂z = cos ( x + y + z )3 x 2 3 z 2cos ( x + y + z ) ∂z ∂y =∂F ∂y ∂F ∂z = cos ( x + y + z )3 y 2 3 z 2cos ( x + y + z ) Substituting all of this into (1), we get ∂z ∂t = cos ( x + y + z )3 x 2 3 z 2cos ( x + y + z ) · 5 cos 5 t + cos ( x + y + z )3 y 2 3 z 2cos ( x + y + z ) · 6 cos 6 t. (2) To answer part (a), we substitute the values ( x, y, z ) = (0 , , z ) and t = 0 into (2) to Fnd ∂z ∂t = cos z 3 z 2cos z 4 · cos 0 + cos z 3 z 2cos z · 6 cos 0 = 10 cos z 3 z 2cos z meters/sec . ±or part (b) we use a calculator to evaluate ∂z ∂t ≈ . 248 m/s, so the bicycle is moving downhill at t = 0. a...
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 Spring '08
 UNKNOWN
 Math, Calculus, Cos, 0.248 m/s

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