Suppose using n = 10 to approximate the integral of a certain function by Simpson's Rule results in an upper bound for the error equal to $\frac { 1 } { 10 }$ . What will the upper bound become if we change to n = 20?
A) $\frac { 1 } { 100 }$
B) $\frac { 1 } { 10,000 }$
C) $\frac { 1 } { 40 }$
D) $\frac { 1 } { 1000 }$
E) $\frac { 1 } { 160 }$
F) $\frac { 1 } { 20 }$
G) $\frac { 1 } { 100,000 }$
H) $\frac { 1 } { 80 }$

Question

Suppose using n = 10 to approximate the integral of a certain function by Simpson's Rule results in an upper bound for the error equal to $\frac { 1 } { 10 }$ . What will the upper bound become if we change to n = 20?
A) $\frac { 1 } { 100 }$ 
B) $\frac { 1 } { 10,000 }$ 
C) $\frac { 1 } { 40 }$ 
D) $\frac { 1 } { 1000 }$ 
E) $\frac { 1 } { 160 }$ 
F) $\frac { 1 } { 20 }$ 
G) $\frac { 1 } { 100,000 }$ 
H) $\frac { 1 } { 80 }$

Quizplus · Accepted Answer

The error in Simpson's Rule is proportional to $\frac{1}{n^4}$. Doubling n from 10 to 20 reduces the error by a factor of $2^4 = 16$. Thus, the new error bound is $\frac{1}{10} \times \frac{1}{16} = \frac{1}{160}$.

Suppose Using N = 10 to Approximate the Integral of a Certain