Quiz 10.9:
Question:
Find an upper bound on the error magnitude in using \( e^x=1+x+\frac{x^2}{2}+\frac{x^3}{6}+\frac{x^4}{24} \) to approximate \( e \)
Solution:
\( f(x)=e^x \)
\( n = 4 \)
\( a=0 \)
\( b=1 \)
\( 0 < c < 1 \)
Therefore, \( \left | R_4(1) \right | = \left | \frac{e^c}{5!}(1-0)^5 \right | < \frac{e}{120} < \frac{3}{120} = \frac{1}{40} \)
