Quiz #8

Name:______________________________

Mathematics 1501
October 28, 1999
Tom Morley

This quiz is one half hour. It is open book and notes,
and caculators are allowed. Show all work and explain your proceedures.

Problem 1 (10 points) . Find the number of function evaluations that will guarantee that Simpson's rule, applied to
[Graphics:quiz8gr1.gif]
[Graphics:quiz8gr2.gif]?

[Graphics:quiz8gr4.gif][Graphics:quiz8gr3.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr5.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr6.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr7.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr8.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr9.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr10.gif]

According to the book on page 489:

[Graphics:quiz8gr4.gif][Graphics:quiz8gr11.gif]

Substitute in values:

[Graphics:quiz8gr4.gif][Graphics:quiz8gr12.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr13.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr14.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr15.gif]

N = 6, Which is 2 n + 1 = 13 function evaluations.

Problem 2 (10 Points) Find the area between the curves
y = [Graphics:quiz8gr16.gif] and y = [Graphics:quiz8gr17.gif]-3[Graphics:quiz8gr18.gif]+3x

[Graphics:quiz8gr4.gif][Graphics:quiz8gr19.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr20.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr21.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr22.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr23.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr24.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr25.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr26.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr27.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr28.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr29.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr30.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr31.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr32.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr33.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr34.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr35.gif]

Problem 3 (10 Points). Find [Graphics:quiz8gr36.gif] [Graphics:quiz8gr37.gif]. Hint use the chain rule.

Chain Rule 

[Graphics:quiz8gr4.gif][Graphics:quiz8gr38.gif]

[Graphics:quiz8gr4.gif][Graphics:quiz8gr39.gif]
[Graphics:quiz8gr4.gif][Graphics:quiz8gr40.gif]