How can Taylor Series help us find a value of h for a specific error tolerance?

[HappyN]

how would you use Taylor Series to answer this:
Find a value of h such that for |x|<h implies sin(x)=x-x^3/6 +x^5/120 + R where |R|< 10^-4?

 

[tiny-tim]

Welcome to PF!

Hi HappyN! Welcome to PF!

(try using the X² icon just above the Reply box )

how would you use Taylor Series to answer this:
Find a value of h such that for |x|<h implies sin(x)=x-x^3/6 +x^5/120 + R where |R|< 10^-4?

Well, those are the first thre terms of the series for sinx (∑ (-x)²ⁿ⁺¹/(2n+1)!) …

so what formula do you know for the remainder? ​

 

[dfillary]

What formula should we know for the remainder?? Am stuck at this point..