Newton'S Method Worksheet
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1WS 10.4 Newton’s Method
Calculus Maximus
Name_________________________________________ Date________________________ Period______
Worksheet 10.4—Newton’s Method
Show all work on a separate sheet of paper. Calculator encouraged.
Free Response & Short Answer
1. What was the name of the other mathematician who independently discovered a similar, more easy-to-
use method for approximating roots around the same time as Newton?
x by finding the positive root for
2
2. Approximate 15 using 3 steps beginning at
4
f x
x
15
.
Show your steps, formulas, and stored values.
Multiple Choice
x , then the next
2
3. If an initial value of 3 is used in Newton’s method to find a solution to
4 0
iterative value is
(A) 1.5
(B) 2.067
(C) 2.167
(D) 2.267
(E) 3.000
3
is found using Newton’s
Iteration
Root value
4. The root of the function
f x
x
4
0
2.0000
method. The successive iterative values of the root are given in
1
1.6667
the table at right. At which iteration would we first achieve an
2
1.5911
accurate root to three decimal places?
3
1.5874
(A) 0
4
1.5874
(B) 1
(C) 2
(D) 3
(E) 4
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