Find an upper bound for the magnitude |E| of the error in the approximation f(x, y) ≈ L(x, y) at the given point over the
given region R.
-$$f ( x , y ) = 4 x + 7 y - 5 \text { at } ( 10 , - 9 ) ; R : | x - 10 | \leq 0.1 , | y + 9 | \leq 0.1$$
A) $| E | \leq 0.01$
B) $| E | \leq 0.04$
C) $| E | \leq 0$
D) $| E | \leq 0.02$

Question

Quizplus · Accepted Answer

The function $f(x, y) = 4x + 7y - 5$ is linear, so the linear approximation $L(x, y)$ is exactly equal to $f(x, y)$ at any point, resulting in zero error.

Find an Upper Bound for the Magnitude |E| of the Error