Question

Calculate the approximate value of root 10 correct to 4 decimal place using taylors theory

Answer 1

Answer:

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−−√|