assign6 - MAT 1322 A Assignment 6 (Due Wed. April 8th at...

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Unformatted text preview: MAT 1322 A Assignment 6 (Due Wed. April 8th at 8:30) Student Number: 1. Find the tangent plane to the surface z = x ln(y ) − 2x + 1 at the point (x, y, z ) = (3, 1, −5) . Work: Answer: z = 2. Find the linear approximation of the function f (x, y ) = (xy 2 + 5)1/3 at the point (x, y ) = (3, 1) and use it to estimate f (2.97, 1.02) . Work: Answers: L(x, y ) = f (2.97, 1.02) s 3. Given that w = ln(x2 + 2y 2 + z ) , x = t cos(2s) , y = and z = t , use the Chain Rule to πt ∂w ∂w find and at the point where t = 1 and s = π . ∂t ∂s Work: Answers: 4. ∂w = ∂t Determine ∂w = ∂s ∂z ∂z and if z is given implicitly as a function of x and y by the equation ∂x ∂y x2 + yez = z 3 . Work: Answers: ∂z = ∂x ∂z = ∂y ...
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assign6 - MAT 1322 A Assignment 6 (Due Wed. April 8th at...

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