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

question 336

Multiple Choice

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.
- $$f ( x , y , z ) = 8 x ^ { 2 } + 7 y ^ { 2 } + 2 z ^ { 2 } \text { at } ( 1 , - 2,3 ) ; R : | x - 1 | \leq 0.1 , | y + 2 | \leq 0.1 , | z - 3 | \leq 0.1$$

• A) \(| E | \leq 0.64\)
• B) \(| \mathrm { E } | \leq 0.72\)
• C) \(| E | \leq 0.96\)
• D) \(| E | \leq 0.48\)

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