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

question 222

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.
- $f ( x , y , z ) = \tan ^ { - 1 } x y z$ at $( 7,7,7 ) ; R : | x - 7 | \leq 0.2 , | y - 7 | \leq 0.2 , | z - 7 | \leq 0.2$

• A) \(| \mathrm { E } | \leq 0.00000021\)
• B) \(| E | \leq 0.00000014\)
• C) \(| E | \leq 0.00000016\)
• D) \(| E | \leq 0.00000027\)

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Definitions:

Self-As-Other Models

Psychological frameworks suggesting individuals can understand and assess themselves by adopting the perspectives of others.

Stereotype

A fixed and oversimplified image or idea of a particular type of person or thing, often based on limited information or false assumptions.

Symbolic Self-Completion

The theory that individuals seek to acquire and display symbols that are associated with their personal goals and identity.

Ego Representation

The aspect of an individual's self-concept that reflects their conscience and the ethical part of personality, guiding behavior through moral judgments.