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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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This note was uploaded on 09/28/2011 for the course MATH 1322 taught by Professor Kousha during the Winter '10 term at University of Ottawa.
 Winter '10
 Kousha
 Approximation, Linear Approximation

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