🟢09b - Fixed Point Iteration Method (Intro): Example 2 and 3

[@20_SinManya]

Sir, in Example 3, another g(x) could've been obtained using the ln x term of the f(x) as follows: g(x) -> 2 - ln x = 0 g(x) -> ln x = 2 g(x) -> x = e^2 g'(x) = 0 < 1, so x (subscript n) would converge However, when we start the iterations using x (subscript n) = g (x subscript (n-1)), we obtain the same constant e^2 in every iteration, which does not lead us to the desired root.

[@SkanCityAcademy_SirJohn]

I see, I guess you omitted something, From x + In(x) - 2 = 0 Using In(x), x = e^(2-x) Derivative w.r.t.x will be -e^(2-x) putting in xo considering the absolute value, you will get 1.6487 which is not less than 1 at xo hence it will not converge

[@Lemon_20502]

Oh yes, sir. Sorry, I missed that 2. My bad! I understood it now. Thanks a lot for clarifying it.

[@SkanCityAcademy_SirJohn]

Most welcome

[@adesiyantope7166]

You’re the best

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@TurkishDoorsEnterpriseGH]

Great. Please do a video on the bracketing method for us. Thank you ❤

[@SkanCityAcademy_SirJohn]

Not yet please

[@solomonmule3414]

so what is the criteria for choosing those numbers to put in the equation to get the interval[a,b]. and can they be different from person to person🙏

[@SkanCityAcademy_SirJohn]

the rule is that f(a) < 0, and f(b) > 0, yes yours can be different from others, but the closer the interval, the closer and more accurate the iterated value

[@CillaDarko]

Very helpful 🙏🏽👏

[@SkanCityAcademy_SirJohn]

Thank you Priscy😍

[@iamtheroze7893]

Excuse me, but 2cos(1.9) is greater than 1 in example 1.

[@SkanCityAcademy_SirJohn]

It's because your calculator was in the degree mode. Kindly put your calculator in the radian mode, and you will have an absolute value of 0.6465.... which is less than 1

[@darindana1045]

@@SkanCityAcademy_SirJohnallways must in radian or not?

[@SkanCityAcademy_SirJohn]

@darindana1045 yes please, in radians

[@darindana1045]

@@SkanCityAcademy_SirJohn my teacher said in degree🥲idk why

[@SkanCityAcademy_SirJohn]

It's supposed to be radians, maybe the question he gave in class requires that it's be solved in degrees.