Problem Statement

{2,6,7}
round(pow(7,-0.25),6)
round(0.614788,1)
pow(0.5,-4) - 7
pow(1,-4) - 7
pow(0.6,-4) - 7
-4*pow(0.6,-5)
round(0.6-0.7160493827160508/-51.440329218107,6)
pow(0.613920,-4)-7
-4*pow(0.613920,-5)
round(0.613920-0.039679263245234075/-45.86707885877791,6)
pow(0.614785,-4)-7
-4*pow(0.614785,-5)
round(0.614785-0.00014360030668569834/-45.54531161499832,6)
round(0.614788,3)

Approximate to three decimal places using Newton's Method and compare with the value from a calculator.

7-1/4

 
Step 1

Newton's Method is used to approximate a root of f(x) = 0.

Question Sequence

Question 1

In order to use this method, we must find a function f(x) that has x = 7-1/4 as a root. If x = 7-1/4, then x-4 = .

Correct.
Incorrect.

 
Step 2

In order to use Newton's method to find a root of f(x) = x-4 - 7, we need an initial guess, x0, which is close to the root, and the formula for Newton's method to generate successive approximations.

Question Sequence

Question 3

Recall the formula for successive approximations.

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 3

To approximate accurately to three decimal places, perform Newton's method several times until the successive approximations agree up to three decimal places.

Question Sequence

Question 6

Find x1.

=

(Round your answer to six decimal places.)

Correct.
Incorrect.

 
Step 4

Question 9

Using a calculator, find the value of 7−1/4 to six decimal places to show that our approximation using Newton's Method is very close to the calculator value.

7−1/4 ≈

Correct.
Incorrect.