Estimate the Error in the Quadratic Approximation of the Given $$f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$$

question 401

Multiple Choice

Estimate the error in the quadratic approximation of the given function at the origin over the given region.
- $$f ( x , y ) = \ln ( 1 + 3 x + 4 y ) , \quad | x | \leq 0.1 , | y | \leq 0.1$$

• A) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.1422\)
• B) \(| \mathrm { E } ( \mathrm { x } , \mathrm { y } ) | \leq 0.2327\)
• C) \(| E ( x , y ) | \leq 0.012\)
• D) \(| E ( x , y ) | \leq 0.1707\)

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Definitions:

Sensory Adaptation

The process by which the sensitivity to a stimulus declines if the stimulus is presented for an extended period of time.

Stimulus

Any event or situation that evokes a response from an organism.

Sensory Apparatus

The complex of sensory organs and parts an organism uses to detect changes in its environment.

Vestibular Receptors

are sensory receptors in the inner ear responsible for detecting movement and changes in the position of the head, important for balance and spatial orientation.