Word Count : 489

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To find the third Taylor polynomial for the function \( f(x, y) = 1 + 5xy + 3^2 y \) at the point \( (1, 2) \), we need to use the general formula for the Taylor series expansion of a function of two variables: \[ T_3(x, y) = f(a, b) + f_x(a, b)(x - a) + f_y(a, b)(y - b) + \frac{1}{2!} f_{xx}(a, b)(x - a)^2 + \frac{1}{2!} f_{yy}(a, b)(y - b)^2 + f_{xy}(a, b)(x - a)(y - b) \] where: - \( f_x \) is the partial derivative of \( f \) with respect to ________ ________ ________ _________ ____ ___ __________ ________ _______ _____.
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