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

question 301

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.
- $$f ( x , y ) = - 4 x ^ { 2 } + 9 y ^ { 2 } - 9 \text { at } ( - 3 , - 2 ) ; R : | x + 3 | \leq 0.1 , | y + 2 | \leq 0.1$$

• A) \(| E | \leq 0.18\)
• B) \(| E | \leq 0.27\)
• C) \(| E | \leq 0.36\)
• D) \(| E | \leq 0.09\)

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Definitions:

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Conditionals

Conditional statements, often found in programming and logic, represent the "if-then" clauses that dictate the outcome based on the fulfillment of a specified condition.

Phonics Instruction

A method of teaching reading and spelling that emphasizes the connection between the letters in written languages and the sounds in spoken languages.

Whole-Language Approach

An educational philosophy emphasizing learning words and sentences in the context of literature rather than through phonics and spelling rules.