Explanation It is given that an function is f ( r , θ ) = r 2 cos 2 θ − r sin θ . Substitute the values r = 3 , θ = π in the function and obtain the value f ( 3 , π ) as follows. f ( 3 , π ) = ( 3 ) 2 cos 2 ( π ) − ( 3 ) sin ( π ) = 9 cos 2 π − 3 sin π = 9 ( 1 ) − 3 ( 0 ) = 9 That is, f ( 3 , π ) = 9 . Substitute the values r = − 2 , θ = π 2 in the function and obtain the value f ( − 2 , π 2 ) as follows

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Chapter 29 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

Ch. 29.1 - Prob. 10E Ch. 29.1 - Prob. 11E Ch. 29.1 - Prob. 12E Ch. 29.1 - Prob. 13E Ch. 29.1 - Prob. 14E Ch. 29.1 - Prob. 15E Ch. 29.1 - Prob. 16E Ch. 29.1 - Prob. 17E Ch. 29.1 - Prob. 18E Ch. 29.1 - Prob. 19E Ch. 29.1 - Prob. 20E Ch. 29.1 - Prob. 21E Ch. 29.1 - Prob. 22E Ch. 29.1 - Prob. 23E Ch. 29.1 - Prob. 24E Ch. 29.1 - Prob. 25E Ch. 29.1 - Prob. 26E Ch. 29.1 - Prob. 27E Ch. 29.1 - Prob. 28E Ch. 29.1 - Prob. 29E Ch. 29.1 - Prob. 30E Ch. 29.1 - Prob. 31E Ch. 29.1 - Prob. 32E Ch. 29.1 - Prob. 33E Ch. 29.1 - Prob. 34E Ch. 29.1 - Prob. 35E Ch. 29.1 - Prob. 36E Ch. 29.1 - Prob. 37E Ch. 29.1 - Prob. 38E Ch. 29.1 - Prob. 39E Ch. 29.1 - Prob. 40E Ch. 29.1 - Prob. 41E Ch. 29.1 - Prob. 42E Ch. 29.1 - Prob. 43E Ch. 29.1 - Prob. 44E Ch. 29.2 - Prob. 1PE Ch. 29.2 - Prob. 2PE Ch. 29.2 - Prob. 1E Ch. 29.2 - Prob. 2E Ch. 29.2 - Prob. 3E Ch. 29.2 - Prob. 4E Ch. 29.2 - Prob. 5E Ch. 29.2 - Prob. 6E Ch. 29.2 - Prob. 7E Ch. 29.2 - Prob. 8E Ch. 29.2 - Prob. 9E Ch. 29.2 - Prob. 10E Ch. 29.2 - Prob. 11E Ch. 29.2 - Prob. 12E Ch. 29.2 - Prob. 13E Ch. 29.2 - Prob. 14E Ch. 29.2 - Prob. 15E Ch. 29.2 - Prob. 16E Ch. 29.2 - Prob. 17E Ch. 29.2 - Prob. 18E Ch. 29.2 - Prob. 19E Ch. 29.2 - Prob. 20E Ch. 29.2 - Prob. 21E Ch. 29.2 - Prob. 22E Ch. 29.2 - Prob. 23E Ch. 29.2 - Prob. 24E Ch. 29.2 - Prob. 25E Ch. 29.2 - Prob. 26E Ch. 29.2 - Prob. 27E Ch. 29.2 - Prob. 28E Ch. 29.2 - Prob. 29E Ch. 29.2 - Prob. 30E Ch. 29.2 - Prob. 31E Ch. 29.2 - Prob. 32E Ch. 29.2 - Prob. 33E Ch. 29.2 - Prob. 34E Ch. 29.2 - Prob. 35E Ch. 29.2 - Prob. 36E Ch. 29.2 - Prob. 37E Ch. 29.2 - Prob. 38E Ch. 29.2 - Prob. 39E Ch. 29.2 - Prob. 40E Ch. 29.2 - Prob. 41E Ch. 29.2 - Prob. 42E Ch. 29.2 - Prob. 43E Ch. 29.2 - Prob. 44E Ch. 29.2 - Prob. 45E Ch. 29.2 - Prob. 46E Ch. 29.3 - If z = 4x2 + x sin y, find ∂z/∂x and ∂z/∂y. Ch. 29.3 - Prob. 2PE Ch. 29.3 - Prob. 1E Ch. 29.3 - Prob. 2E Ch. 29.3 - Prob. 3E Ch. 29.3 - Prob. 4E Ch. 29.3 - Prob. 5E Ch. 29.3 - Prob. 6E Ch. 29.3 - Prob. 7E Ch. 29.3 - Prob. 8E Ch. 29.3 - Prob. 9E Ch. 29.3 - Prob. 10E Ch. 29.3 - Prob. 11E Ch. 29.3 - Prob. 12E Ch. 29.3 - Prob. 13E Ch. 29.3 - Prob. 14E Ch. 29.3 - Prob. 15E Ch. 29.3 - Prob. 16E Ch. 29.3 - Prob. 17E Ch. 29.3 - Prob. 18E Ch. 29.3 - Prob. 19E Ch. 29.3 - Prob. 20E Ch. 29.3 - Prob. 21E Ch. 29.3 - Prob. 22E Ch. 29.3 - Prob. 23E Ch. 29.3 - Prob. 24E Ch. 29.3 - Prob. 25E Ch. 29.3 - Prob. 26E Ch. 29.3 - Prob. 27E Ch. 29.3 - Prob. 28E Ch. 29.3 - Prob. 29E Ch. 29.3 - Prob. 30E Ch. 29.3 - Prob. 31E Ch. 29.3 - Prob. 32E Ch. 29.3 - Prob. 33E Ch. 29.3 - Prob. 34E Ch. 29.3 - Prob. 35E Ch. 29.3 - Prob. 36E Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - Prob. 39E Ch. 29.3 - Prob. 40E Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - Prob. 42E Ch. 29.3 - Prob. 43E Ch. 29.3 - Prob. 44E Ch. 29.3 - Prob. 45E Ch. 29.3 - Prob. 46E Ch. 29.3 - Prob. 47E Ch. 29.3 - Prob. 48E Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.3 - In Exercises 35–50, solve the given...Ch. 29.4 - Prob. 1PE Ch. 29.4 - Prob. 1E Ch. 29.4 - Prob. 2E Ch. 29.4 - Prob. 3E Ch. 29.4 - Prob. 4E Ch. 29.4 - Prob. 5E Ch. 29.4 - In Exercises 5–18, evaluate the given double...Ch. 29.4 - Prob. 7E Ch. 29.4 - Prob. 8E Ch. 29.4 - Prob. 9E Ch. 29.4 - Prob. 10E Ch. 29.4 - Prob. 11E Ch. 29.4 - Prob. 12E Ch. 29.4 - Prob. 13E Ch. 29.4 - Prob. 14E Ch. 29.4 - Prob. 15E Ch. 29.4 - Prob. 16E Ch. 29.4 - Prob. 17E Ch. 29.4 - Prob. 18E Ch. 29.4 - Prob. 19E Ch. 29.4 - Prob. 20E Ch. 29.4 - Prob. 21E Ch. 29.4 - Prob. 22E Ch. 29.4 - Prob. 23E Ch. 29.4 - Prob. 24E Ch. 29.4 - Prob. 25E Ch. 29.4 - Prob. 26E Ch. 29.4 - Prob. 27E Ch. 29.4 - Prob. 28E Ch. 29.4 - Prob. 29E Ch. 29.4 - Prob. 30E Ch. 29.4 - Prob. 31E Ch. 29.4 - Prob. 32E Ch. 29.4 - Prob. 33E Ch. 29.4 - Prob. 34E Ch. 29 - Prob. 1RE Ch. 29 - Prob. 2RE Ch. 29 - Prob. 3RE Ch. 29 - Prob. 4RE Ch. 29 - Prob. 5RE Ch. 29 - Prob. 6RE Ch. 29 - Prob. 7RE Ch. 29 - Prob. 8RE Ch. 29 - Prob. 9RE Ch. 29 - Prob. 10RE Ch. 29 - Prob. 11RE Ch. 29 - Prob. 12RE Ch. 29 - Prob. 13RE Ch. 29 - Prob. 14RE Ch. 29 - Prob. 15RE Ch. 29 - Prob. 16RE Ch. 29 - Prob. 17RE Ch. 29 - Prob. 18RE Ch. 29 - Prob. 19RE Ch. 29 - Prob. 20RE Ch. 29 - Prob. 21RE Ch. 29 - Prob. 22RE Ch. 29 - Prob. 23RE Ch. 29 - Prob. 24RE Ch. 29 - Prob. 25RE Ch. 29 - Prob. 26RE Ch. 29 - Prob. 27RE Ch. 29 - Prob. 28RE Ch. 29 - Prob. 29RE Ch. 29 - Prob. 30RE Ch. 29 - Prob. 31RE Ch. 29 - Prob. 32RE Ch. 29 - Prob. 33RE Ch. 29 - Prob. 34RE Ch. 29 - Prob. 35RE Ch. 29 - Prob. 36RE Ch. 29 - Prob. 37RE Ch. 29 - Prob. 38RE Ch. 29 - Prob. 39RE Ch. 29 - Prob. 40RE Ch. 29 - Prob. 41RE Ch. 29 - Prob. 42RE Ch. 29 - Prob. 43RE Ch. 29 - Prob. 44RE Ch. 29 - Prob. 45RE Ch. 29 - Prob. 46RE Ch. 29 - Prob. 47RE Ch. 29 - Prob. 48RE Ch. 29 - Prob. 49RE Ch. 29 - Prob. 50RE Ch. 29 - Prob. 51RE Ch. 29 - Prob. 52RE Ch. 29 - Prob. 53RE Ch. 29 - Prob. 54RE Ch. 29 - Prob. 55RE Ch. 29 - Prob. 1PT Ch. 29 - Prob. 2PT Ch. 29 - Prob. 3PT Ch. 29 - Prob. 4PT Ch. 29 - Prob. 5PT Ch. 29 - Prob. 6PT Ch. 29 - Prob. 7PT Ch. 29 - Prob. 8PT

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The values of f ( 3 , π ) and f ( − 2 , π 2 ) .

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