At the end of the course, each student should be able to…
- S06: Lineariz. Compute the linearization of a two-variable real-valued function at a point and use it for approximation.
- Differentiable functions \(f(x,y)\) may be approximated near a
point \(P_0\) by the linearization \(L(x,y)\) defined by the
tangent plane at that point.
- Its equation is \(L(x,y)=f(P_0)+f_x(P_0)(x-x_0)+f_y(P_0)(y-y_0)\).
- Thus if \(<x,y>\approx P_0\), then \(L(x,y)\approx f(x,y)\).
- University Calculus: Early Transcendentals (3rd Ed)
- 13.6 (exercises 25-30)