Question

Find the positive root of the equation 3x-cosx-1 using Regula Falsi method and correct upto 4 decimal

places.

a) 0.6071 ( correct upto 4 decimal)

b) 0.5071

c) 0.6071 (correct to 4 significant fig)

d) 0.5701​

Answer 1

Answer:

0.5071 options c is a correct answer

Answer 2

Answer:

so, the value of root is 0.6071.

Option(c) is correct.

Step-by-step explanation:

f(x) = 3x - Cos(x) - 1 = 0

f(-60) = -0.025

f(0.61) = 0.01

First approximation

x              y

60           -0.025

.61             0.01

Difference

0.01            0.035

h1 = $\frac{0.01(0.025)}{0.035}$

 = 0.007

x1 = 0.060+0.007

   = .607

Second approximation

0.607        - 0.00036

0.608         0.00321

Difference

0.001           0.00357

h2 = $\frac{0.001(0.00036)}{0.00357}$

    = 0.0001

x2 = 0.607 + 0.001

     = 0.6071

Third approximation

0.6071                0.00000

0.6072               0.00035

Difference

0.0001                0.00035

h3= 0

x3 = 0.6071

Since x2 = x3

so, the value of root is 0.6071.

Option(c) is correct.