Solve the Problem $1 + 8 x + 28 x ^ { 2 }$

question 245

Multiple Choice

Solve the problem.
-The polynomial $1 + 8 x + 28 x ^ { 2 }$ is used to approximate $f ( x ) = ( 1 + x ) ^ { 8 }$ on the interval $- 0.01 \leq x \leq 0.01$ . Use the Remainder Estimation Theorem to estimate the maximum absolute error.

• A) \(\approx 3.642 \times 10 ^ { - 5 }\)
• B) \(\approx 5.886 \times 10 ^ { - 5 }\)
• C) \(\approx 5.886 \times 10 ^ { - 4 }\)

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Definitions:

Major Calyx

A major calyx is a component of the kidney, which acts as a chamber that collects urine from the minor calyces and transports it to the renal pelvis.

Renal Cortex

The outer portion of the kidney between the renal capsule and the renal medulla that functions in the filtration of blood to form urine.

Genital Papilla

A small, fleshy protrusion often found near the reproductive organs in both sexes of various animals, particularly noticeable in fish as part of their external genitalia.

Urogenital Orifice

An external opening in certain animals through which both urinary and genital tracts discharge.