# Error bounds

1. Oct 24, 2006

### 413

a) With f(x)= e^-x^2 , compute approximations using midpoint, trapezoidal and simpson's rule with n=2.
I found that from midpoint rule gives 0.88420, trapezoidal rule gives 0.87704, and simpson's rule gives 0.82994.

Compute the error esimates for midpoint, trapezoidal, simpson's. Carefully examine the extreme values of f ''(x). You may use that |f ''''(x)| < 12 for 0<x< 2. (the < signs all mean less than or equal to).
I found that EM=0.14875, ET=0.07438, ES=0.13333

My question is how big should we take n to guarntee absolute value of ET <0.0001? and for EM<0.0001 and ES<0.0001?
How would you figure this question out?

2. Oct 25, 2006

### jkh4

for how big should take n to guarntee absolute value

for example with ET <0.0001 plug in all the value for K, a, b

so in your case, K is 2, a is 0, b is 2

so it would be (2*2^3)/(12n^2) < 0.0001 and just do it as algebra question

(2*2^3)/(12*0.0001) < n^2 and find the square root of n

just curious, are you also taking MATH 152 in SFU? coz i did this question too =)