Answer:
Claire owed Martha $8 she originally owed Martha 12 but already gave her 4 this was a problem for Claire considering she only got $4 a week
If <em>f(x)</em> = 7/(1<em> </em>+ <em>x</em>), then
<em>f</em> (2) = 7/3
<em>f '(x)</em> = -7/(<em>x</em> + 1)² ==> <em>f '</em> (2) = -7/9
<em>f ''(x)</em> = 14/(<em>x</em> + 1)³ ==> <em>f ''</em> (2) = 14/27
<em>f '''(x)</em> = -42/(<em>x</em> + 1)⁴ ==> <em>f '''</em> (2) = -14/27
Then the Taylor series of <em>f(x)</em> about <em>a</em> = 2 is
7/3 + 1/1! (-7/9) (<em>x</em> - 2) + 1/2! (14/27) (<em>x</em> - 2)² + 1/3! (-14/27) (<em>x</em> - 2)³
= 7/3 - 7/9 (<em>x</em> - 2) + 7/27 (<em>x</em> - 2)² - 7/81 (<em>x</em> - 2)³
The answer for this equation is 25
-4 ...............................
