Question 1-3 are solved and attached below. Let m know if you need any revisions.

MATH 2414 (8.8)

Name:

Worksheet # 13

Estimation

1) Consider the function f(x)

x*

=

-

6x

+8

on

the interval

[5, 8] with 10 subintervals.

Using only a calculator, find the LRTMS approximations.
An b - a

vide

8-S

s,s)

nt.

-0:3

&q=
nalo Swbintunas

LEd poid

+ ) s|f(1)+A(a)+

f(1.)|

- 03 (31s02s)-15 4071s
Riat End pcsv*
2 0(70.05) = 2ol-olS

=hfl1HA) +)+f()tf(1)
2

0:3

-

(!5D.s12 t 35 02s4S

66

S mpsm Ral

Cfe)14(f6D+H%)+f()+K(*) +4,))
ta(Hn)Hna)t. f(ra) +H()
17:75

Page 1 of4

2)

Calculate

errorbounds

onthe interval [12, 27]

Rule for
for Trapezoid, Midpoint and Simpson's

with

n

f(x)

=

x'

-6x

+8

=20.

z i d Rl
b-

27-12-= lS

E7SCb-a
20

2-n

fla)f(A-La+S) -3n12.

)
So

f (3n-2).

maimwm Vame J12,27

l

5

MidpenHR

lEM

(15)

i

6-12
SD

at

1*27

o546

2 X20

()1sD(1 s S273
24n

4(2-0

Errbrrd fos Simpsm Twe.

ETTerbord Es

0X

(27-12)
2-x n

Page 2 of4

3) For h(x)= -2 sin(3r) on [1, 5] find the minimum number of subintervals needed to be
accurate within .001 for Trapezoid, Midpoint and Simpson's Rule.

hC)sn(3)
18sinCs)

h"C

6 Gs C3)

h'Cn)

hC= 54 as()

C)- 162Sin(s).

|*')- |IeSw (3 -

C

4.6587

Fos ...