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Find the linear approximation for T(z, y) in proximity of (x₀, y₀) and express it as T(x, y) = a+b •(x-p)+c•(y-q) a. The coefficient a is equal to ___ b. The coefficient b is equal to ___ c. The coefficient c is equal to ___

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Final answer:

The linear approximation of the function T(x, y) is found by using its value and its partial derivatives at a point (x₀, y₀) which gives the coefficients a, b, and c for the approximation.

Step-by-step explanation:

The task is to find the linear approximation of a function T(x, y) near a point (x₀, y₀). The linear approximation can be written in the form T(x, y) = a + b • (x - p) + c • (y - q), where p and q are the coordinates of the point of approximation (x₀, y₀).

To find the coefficients a, b, and c, we use the value of the function and its partial derivatives at the point of approximation.

The coefficient a is the value of the function T at (x₀, y₀), the coefficient b is the partial derivative of T with respect to x evaluated at (x₀, y₀), and the coefficient c is the partial derivative of T with respect to y evaluated at (x₀, y₀).

In this problem, the provided information does not give values for x₀, y₀, or T directly but presumably these would be given in the actual problem or could be calculated based on additional information.

User Seb Rose
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