Question

find the root of the equation cos x-2x+3=0, correct to three decimal places​

Answer 1

Given :   cos x-2x+3=0

To Find : root of the equation correct to three decimal places​

Solution:

cos x-2x+3=0

-1 ≤ cos x ≤ 1

-2x+3 =  -cos x

-1 ≤  -2x+3  ≤ 1

=> -4 ≤  -2x ≤ - 2

=> 2 ≥ x  ≥ 1

1  ≤  x  ≤  2

using bisection method

x               cos x-2x+3

1    1.540302306

2   -1.416146837

1.5   0.070737202

1.75  -0.678246056

1.625 -0.304177135

1.5625 -0.116703768

1.53125 -0.02296398

1.515625 0.023893342

1.5234375 0.000466126

1.52734375 -0.011248596

1.525390625 -0.005391149

1.524414063 -0.002462489

1.523925781 -0.000998176

1.523681641 -0.000266024

1.52355957 0.000100051

1.523620605 -8.29863E-05

root of the equation cos x-2x+3=0 is   1.523 correct to three decimal places

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