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Chapter 8: Applications of Derivatives
Approximating Roots Using
Newton’s Method
516–518 Find the root using Newton’s method.
516. Use Newton’s method to find the root of
cos x = x correct to five decimal places.
517. Use Newton’s method to find the root
of x
3
– x
2
– 2 in the interval [1, 2] correct
to five decimal places.
518. Use Newton’s method to find the positive
root of x
x
+ =
1
2 correct to five decimal
places.
Doing Approximations Using
Newton’s Method
513–515 Find the fifth approximation of the root of
the equation using the given first approximation.
513. x
3
+ 4x – 4 = 0 using x 1 = 1. Round the solution
to the fifth decimal place.
514. x
4
– 18 = 0 using x 1 = 2. Round the solution to
the seventh decimal place.
515. x
5
+ 3 = 0 using x 1 = –1. Round the answer to
the seventh decimal place.