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

question 75

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.
- $f ( x , y ) = \ln ( 8 x + 7 y )$ at $( 1,1 ) ; R : | x - 1 | \leq 0.1 , | y - 1 | \leq 0.1$

• A) \(| \mathrm { E } | \leq 0.007\)
• B) \(| \mathrm { E } | \leq 0.0057\)
• C) \(| E | \leq 0.0089\)
• D) \(| \mathrm { E } | \leq 0.0047\)

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Definitions:

Confidence Interval

A set of values, obtained from sample data, that probably includes the value of an unspecified population parameter, given a certain confidence level.

Point Estimate

A solitary figure or statistical measure employed to approximate the worth of a population parameter.

Confidence Interval

A portfolio of values, extracted from sampling efforts, believed to encapsulate the undiscovered value of a population attribute.

Normal Distribution

A balanced probability distribution around the mean, demonstrating that occurrences are more frequent near the mean than away from it.