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