quiz05' - e sin ) + (1)( e cos ) = e s 2 + t 2 (2 s sin(...

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Quiz 5 Solutions 1. Find the tangent plane for z = e sin 2 x +cos 2 y - 1 at the point ( π, π, 1). ∂z ∂x = 2 z sin x cos x and ∂z ∂y = - 2 z sin y cos y . So, the tangent plane is given by z - 1 = 0 · ( x - π ) + 0 · ( x - π ) = 0, or z = 1. 2. Find ∂z ∂s and ∂z ∂t in terms of s and t only, where z = e α sin β , α = s 2 + t 2 , and β = s - 2 t . ∂z ∂s = ∂α ∂s ∂z ∂α + ∂β ∂s ∂z ∂β = (2 s )(
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Unformatted text preview: e sin ) + (1)( e cos ) = e s 2 + t 2 (2 s sin( s-2 t ) + cos( s-2 t )) . z t = t z + t z = (2 t )( e sin ) + (-2)( e cos ) = 2 e s 2 + t 2 ( t sin( s-2 t )-cos( s-2 t )) . 1...
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