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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Definitions:

Planning Budget

A financial plan that outlines the expected revenues, expenses, and goals of an organization for a specific period.

Other Expenses

Costs not directly related to the production of goods or services, such as interest payments or losses from asset sales.

Activity Variance

The difference between the budgeted amount of activity and the actual amount of activity, often analyzed in budgeting and costing practices.

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