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

question 4

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.
- $$f ( x , y ) = 9 x ^ { 2 } y ^ { 3 } \text { at } ( 2,1 ) ; R : | x - 2 | \leq 0.2 , | y - 1 | \leq 0.2$$

• A) \(| E | \leq 13.68576\)
• B) \(| \mathrm { E } | \leq 19.65492\)
• C) \(| \mathrm { E } | \leq 25.09056\)
• D) \(| \mathrm { E } | \leq 19.38816\)

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Definitions:

Anorexia Nervosa

An eating disorder characterized by an obsessive fear of gaining weight, leading to severe restrictions on food intake and often resulting in dangerous weight loss.

Bulimia Nervosa

Bulimia nervosa is an eating disorder characterized by episodes of binge eating followed by compensatory behaviors such as vomiting, fasting, or excessive exercise.

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Any encounter or activity involving sexual intimacy, exploration, or expression.

Obsessive Qualities

Refers to the persistent and intrusive thoughts, urges, or images that cause significant anxiety or distress.