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

question 295

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.
- $$f ( x , y , z ) = \ln ( 2 x + 4 y + 2 z ) \text { at } ( 1,1,1 ) ; R : | x - 1 | \leq 0.1 , | y - 1 | \leq 0.1 , | z - 1 | \leq 0.1$$

• A) \(| E | \leq 0.0167\)
• B) \(| E | \leq 0.0156\)
• C) \(| E | \leq 0.0139\)
• D) \(| \mathrm { E } | \leq 0.0208\)

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