Question

value of √10 using taylors theorom​

Answer 1

Answer:

I need to calculate 5–√ using taylor series to the accuracy of 3 digit after the point (0.5∗10−3).

I defined :

f(x)=x−−√

Therefore :

f′(x)=12x−−√

f′′(x)=−14x3−−√

f′′′(x)=38x5−−√

for x=5 :

|R2(5)|=∣∣∣f(3)(c)3!∣∣∣=∣∣∣∣18c5√3!∣∣∣∣∣∣∣13!∗8c5−−√∣∣∣

I got stuck now, how can I evaluate:

???≥|3!∗8c5−−√|

Also, I wonder how many derivatives I need to calculate inorder to reach to the required accuracy, is there a way to find out?

I just took an arbitrary guess to the third derivative.

Any help will be appreciated.

Please relate with route10

Thank me later