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
Ай бұрын
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
Ай бұрын
Oh yes, sir. Sorry, I missed that 2. My bad! I understood it now. Thanks a lot for clarifying it.
@SkanCityAcademy_SirJohn
Ай бұрын
Most welcome
@shalomayooluwa
14 күн бұрын
Well explained 💯💯
@SkanCityAcademy_SirJohn
14 күн бұрын
Thanks so much
@adesiyantope7166
4 ай бұрын
You’re the best
@SkanCityAcademy_SirJohn
4 ай бұрын
Thanks so so much
@TurkishDoorsEnterpriseGH
7 ай бұрын
Great. Please do a video on the bracketing method for us. Thank you ❤
@SkanCityAcademy_SirJohn
7 ай бұрын
Not yet please
@collinsgichangi5421
3 күн бұрын
How is 2sin(1.9) that answer I think there is an error there 2sin(1.9) is 0.00663(6s.f)
@SkanCityAcademy_SirJohn
3 күн бұрын
Your calculator should be in the radians mode and not the degree mode. Thanks
@solomonmule3414
4 ай бұрын
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
4 ай бұрын
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
10 ай бұрын
Very helpful 🙏🏽👏
@SkanCityAcademy_SirJohn
10 ай бұрын
Thank you Priscy😍
@iamtheroze7893
5 ай бұрын
Excuse me, but 2cos(1.9) is greater than 1 in example 1.
@SkanCityAcademy_SirJohn
5 ай бұрын
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
4 ай бұрын
@@SkanCityAcademy_SirJohnallways must in radian or not?
@SkanCityAcademy_SirJohn
4 ай бұрын
@darindana1045 yes please, in radians
@darindana1045
4 ай бұрын
@@SkanCityAcademy_SirJohn my teacher said in degree🥲idk why
@SkanCityAcademy_SirJohn
4 ай бұрын
It's supposed to be radians, maybe the question he gave in class requires that it's be solved in degrees.
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