Question

Let f(x, y) = x² / 2+1 Use the Linear Approximation at an appropriate point (a, b) to estimate f(5.04, 1.91).

So, f(5.04, 1.91) = _________________

Answer 1

To estimate f(5.04, 1.91) using the linear approximation, find an appropriate starting point and use the linear approximation formula.

Step-by-step explanation:

To estimate f(5.04, 1.91) using the linear approximation, we need to find an appropriate point (a, b) to use as a starting point. Let's choose (5, 2) as our starting point. The linear approximation formula is given by f(x, y) = f(a, b) + f_x(a, b)(x - a) + f_y(a, b)(y - b). First, find the partial derivatives of f with respect to x and y. Then, substitute the given values into the formula to find the estimate of f(5.04, 1.91).