Provide an Appropriate Response Be a Quadratic Approximation To $\mathrm { f } ( \mathrm { x } )$

question 390

Essay

Provide an appropriate response.
-Let $\mathrm { Q } ( \mathrm { x } ) = \mathrm { b } _ { \mathrm { O } } + \mathrm { b } _ { 1 } ( \mathrm { x } - \mathrm { a } ) + \mathrm { b } _ { 2 } ( \mathrm { x } - \mathrm { a } ) ^ { 2 }$ be a quadratic approximation to $\mathrm { f } ( \mathrm { x } )$ at $x = a$ with the properties:
i. $Q ( a ) = f ( a )$
ii. $Q ^ { \prime } ( a ) = f ^ { \prime } ( a )$
iii. $\mathrm { Q } ^ { \prime \prime } ( \mathrm { a } ) = \mathrm { f } ^ { \prime \prime } ( \mathrm { a } )$
(a) Find the quadratic approximation to $f ( x ) = \frac { 1 } { 4 + x }$ at $x = 0$ .
(b) Do you expect the quadratic approximation to be more or less accurate than the linearization? Give reasons fc answer.

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Definitions:

Retroversion

The tilting backward of an organ or part, such as the uterus, from its normal position.

Anteflexion

The bending forward of an organ or part of the body.

Anteversion

A forward tilting of an organ, such as the uterus, from its normal position.

Minipill

A type of birth control pill that contains only progesterone and is taken to prevent pregnancy.