How do I go about estimating a certain function to within an certain error?

If you wanted to estimate e^0.1 to within 0.0001 would you use the Maclaurin Series Theorem?

If so... the Maclaurin Series for e^x is

e^x = 1 + x/1! + x^2/2! + ... + x^n/n!

We want e^x to within 0.0001. So intuition tells me that I am going to have to express e^x as it Maclaurin series with at least four terms.

e^0.1 = 1.105170918...
e^0.1 = 1 + 0.1/1! + 0.1^2/2! + 0.3^3/3! = 1.10516666...

Is this the correct estimation of e^0.1 to within 0.0001?

Thankyou for any help!

Cheers. Ben.

There are several ways of approximating functions, such as MacLaurin (Taylor) or Fourier expansions. The Taylor expansion is useful since there are "explicit" expressions for the error you make. Personally, I would use the approach you proposed too.

Bye!

Crisp