According to Taylor's Formula, What Is the Maximum Error Possible $\sum _ { n = 0 } ^ { 4 } \frac { x ^ { n } } { n ! }$

Multiple Choice

According to Taylor's Formula, what is the maximum error possible in the use of the sum $\sum _ { n = 0 } ^ { 4 } \frac { x ^ { n } } { n ! }$ to approximate $e ^ { x }$ in the interval $- 1 \leq x \leq 1$ ?

A) $\frac { e } { 240 }$
B) $\frac { e } { 48 }$
C) $\frac { e } { 480 }$
D) $\frac { e } { 24 }$
E) $\frac { e } { 20 }$
F) $\frac { e } { 120 }$
G) $\frac { e } { 12 }$
H) $\frac { e } { 60 }$