Math Problem Statement

carilah persamaan-persamaan untuk bidang singgung dan garis normal pada permukaan z=x^2+y^2 di titik (2, -1, 5)

Solution

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Math Problem Analysis

Mathematical Concepts

Differential Calculus
Multivariable Calculus
Gradient
Tangent Planes
Normal Lines

Formulas

Gradient: ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Tangent Plane: A(x - x0) + B(y - y0) + C(z - z0) = 0
Normal Line Parametric Equations: x = x0 + At, y = y0 + Bt, z = z0 + Ct

Theorems

Gradient Vector and Directional Derivatives

Suitable Grade Level

Grades 11-12, Undergraduate Calculus