Question

Use difference quotients with delta x = 0.1 and delta y = 0.1 to estimate fx(1, 2) and fy(1, 2).

Answer 1

To estimate fx(1, 2) and fy(1, 2), use the difference quotient formula with delta x = 0.1 and delta y = 0.1. Substitute the given values for f(x, y) to obtain the estimates.

Step-by-step explanation:

To estimate fx(1, 2), we can use the difference quotient formula:

fx(x, y) ≈ (f(x + delta x, y) - f(x, y))/delta x

Substituting the values x = 1 and y = 2, and using delta x = 0.1, we get:

fx(1, 2) ≈ (f(1 + 0.1, 2) - f(1, 2))/0.1

We can use the same approach to estimate fy(1, 2), but this time using delta y = 0.1:

fy(1, 2) ≈ (f(1, 2 + 0.1) - f(1, 2))/0.1

To obtain the final estimates, you'll need to substitute the given values for f(x, y) in the above formulas.