Question

A) Find the linearization of the functionf(x,y)=\sqrt{46-x^2-4y^2}at the point (1,3). L(x,y) =

b). Use the linear approximation to estimate the value of f(0.9,-2.9)
f(0.9,-2.9) =

Answer 1

To answer the student's question, apply the formula for linearization which involves partial derivatives of the function at the given point, resulting in the linear approximation which can be used to estimate the function's value at nearby points.

Step-by-step explanation:

The question involves finding the linearization of a two-variable function at a given point and using it to approximate the value of the function at a nearby point. To find the linearization, we calculate the partial derivatives at the given point and use the formula L(x,y) = f(a,b) + f_x(a,b)(x - a) + f_y(a,b)(y - b), where f_x and f_y are the partial derivatives with respect to x and y respectively, and (a,b) is the point of linearization. When we apply this process to the function f(x,y) = \sqrt{46 - x^2 - 4y^2} at the point (1,3), we obtain the linear function L(x,y) which can be used to estimate f(0.9, -2.9).