Approximation Using Taylor POlynomial

[e179285]

Find an approximate value of the number e^-0.1 with an error less than 10^-3

ı know that e^x = Ʃ(from zero to ınfinity) xⁿ / n!=1+x/1!+x
²/2!+...

ı don't know how to use e^-0.1 in this question.Do ı write -0.1 instead of x in e^x series?

 

[tiny-tim]

ı know that e^x = Ʃ(from zero to ınfinity) xⁿ / n!=1+x/1!+x
²/2!+...

ı don't know how to use e^-0.1 in this question.Do ı write -0.1 instead of x in e^x series?

yup!

 

[Vargo]

Since you are asked to calculate to within a particular accuracy, what you need is not the Taylor series, but a Taylor polynomial plus remainder estimate.