«Я ушла, потому что с меня хватит»: как муж одним вечером перевернул мою жизнь — и поселил в нашем доме чужих детей
Мы с Антоном познакомились, когда его брак уже давно походил на развалины советского сарая — всё рухнуло, но пыль ещё не осела. Он был свободен, разведён, жил один в своей однушке и казался образцом спокойствия — как самовар перед закипанием. Мне тогда почудилось, что это тот самый человек, с которым можно построить крепкую избу на века. О бывшей жене он не упоминал ни словом — буд00:01 In this question, we need to find out the taylor series, okay, for the function f of x is equals to cos of x and about the point a is equals to 5 by 3.
00:14 So, first of all, i will write down the formula for the taylor series.
00:18 So, taylor series centered at a is equals to 5 by 3, it looks like f of x is equals to summation n going from 0 to infinity nth derivative at the point a divided by n factorial times x minus a raised to n.
00:43 Correct? so, this is the general formula for the taylor series.
00:46 Since here our a value is 5 by 3, so it becomes n going from 0 to infinity nth derivative at 5 by 3 over n factorial times x minus 5 by 3 raised to n.
01:02 Correct.
01:03 Now, we have to find out the coefficient.
01:05 So, first of all, we consider f of x is equals to cos of x.
01:11 So, f at 5 by 3 will be cos of 5 by 3 and we know it is 1 over 2.
01:18 Then if i find the first derivative, it is minus sine x.
01:22 So, at 5 by 3, it will be minus sine of 5 by 3 and sine of 5 by 3 is root 3 over 2.
01:31 So, minus root 3 over 2.
01:33 The second derivative, it is minus cos of x.
01:37 So, at 5 by 3, it will be minus cos of 5 by 3, which is minus 1 over 2.
01:46 Then third derivative is sine of x.
01:50 Evaluating at 5 by 3, we get sine of 5 by 3, which is root 3 over 2.
01:55 Then fourth derivative comes out to be cos of x.
01:59 Evaluating at 5 by 3, we get 1 over 2.
02:04 And from here, we can see that this thing is repeating.
02:06 So, fifth derivative will be same as the first derivative which is minus sine x.
02:13 At 5 by 3, it is minus root 3 over 2…
