Given the function f(x) = 4x3 sin(x) — 1, 0 ≤ x ≤ 2л has a solution a in the interval (0.7, 0.8) given in radians. An iterative formula, of the form given below, is used to find a. Xn+1 = A + B sin(xn), x1 = 0.75 where A and B are constants. a) Find out the values of A and B in terms of fractions. A = and B = b) Find the values of x2 and x3 correct to 4 decimal places. x2 = x3 =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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Given the function
f(x) = 4x3 sin(x) — 1,
0 ≤ x ≤ 2л
has a solution a in the interval (0.7, 0.8) given in radians.
An iterative formula, of the form given below, is used to find a.
Xn+1 = A + B sin(xn), x1 = 0.75
where A and B are constants.
a) Find out the values of A and B in terms of fractions.
A =
and B =
b) Find the values of x2 and x3 correct to 4 decimal places.
x2 =
x3 =
Transcribed Image Text:Given the function f(x) = 4x3 sin(x) — 1, 0 ≤ x ≤ 2л has a solution a in the interval (0.7, 0.8) given in radians. An iterative formula, of the form given below, is used to find a. Xn+1 = A + B sin(xn), x1 = 0.75 where A and B are constants. a) Find out the values of A and B in terms of fractions. A = and B = b) Find the values of x2 and x3 correct to 4 decimal places. x2 = x3 =
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