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Unformatted text preview: x − 2) + 8( y − 1) = 0 which simpliFes to 8 y = 16 − 4 x or y = − x 2 + 2. The level curve is an ellipse whose intersects are ( ± √ 8 , 0) and (0 , ± √ 2). The gradient vector is perpendicular to the tangent line at (2 , 1) and it points to the outside of the ellipse. 2. (5 points) Find all the second partial derivatives of the function u ( s, t ) = es sin t . Solution. The ±rst partial derivatives are the following u s = − es sin t and u t = es cos t The second partial derivatives are u ss = es sin t, u tt = − es sin t, u st = u ts = − es cos t...
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 Fall '08
 Helton
 Math, Derivative, Vector Calculus, Gradient, Jacobian matrix and determinant, gradient vector

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