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

question 211

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.
- $$f ( x , y , z ) = e ^ { 9 x + 7 y + 5 z } \text { at } ( 0,0,0 ) ; R : | x | \leq 0.1 , | y | \leq 0.1 , | z | \leq 0.1$$

• A) \(| E | \leq 34.3959\)
• B) \(| E | \leq 27.7813\)
• C) \(| E | \leq 29.7657\)
• D) \(| E | \leq 31.7501\)

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Definitions:

Phasic Receptors

Sensory receptors that quickly respond to stimuli but then adapt and decrease their response over time.

Proprioceptors

Sensory receptors located in muscles, tendons, and joint capsules that provide information about body position and movement.

Moving Hand

The complex motor function involving the muscles, bones, and nerves of the hand, enabling manipulation and movement.

Proprioception

The sense of the relative position of body parts and strength of effort being employed in movement.