Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Linearization
Partial Derivatives
Formulas
L(x, y, z) = f(x_0, y_0, z_0) + f_x(x_0, y_0, z_0)(x - x_0) + f_y(x_0, y_0, z_0)(y - y_0) + f_z(x_0, y_0, z_0)(z - z_0)
Partial derivatives: f_x = x/sqrt(x^2 + y^2 + z^2), f_y = y/sqrt(x^2 + y^2 + z^2), f_z = z/sqrt(x^2 + y^2 + z^2)
Theorems
Multivariable Function Linearization Theorem
Suitable Grade Level
Undergraduate Calculus
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