Question

use bisection method, find real roots for equarion ex=10x correct to 3 decimal places​

Answer 1

The bisection method to find real roots for equarion ex=10x correct to 3 decimal places​ is given as follows.

Given,

f(x) = e^x - 10x

Now consider,

f(0) = e^0 - 10 (0) = 1 - 10 = -9 < 0

f(4) = e^4 - 10 (4) = 54.59 - 40 = 14.59 > 0

Therefore, the roots lie between 0 and 4.

a = 0 and b = 4

c = a+b / 2 = 0+4 /2 = 2

f(c) = e^2 - 10 (2) = -12.61 < 0

So, we replace a with - 12.61

a = -12.61 and b = 4

f(-12.61) = e^(-12.61) - 10 ( -12.61) = 126.1

f(4) = e^4 - 10 (4) = 14.59