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I'm having trouble with this question and was wondering if someone could give me hints or suggestions on how to solve it. Any help would be greatly appreciated thankyou! :)

Find the Taylor polynomial of degree 3 of f (x) = e^x

about x = 0 and hence find an approximate value for e. Give an estimate for the error in the approximation.

I know from following the Big O Notation...

e^x = 1 + x + (x^2) / 2! + (x^3) / 3! + ... + (x^n) / n! + O (x^(n+1))

So I'm thinking for a polynomial of degree 3 we have...

e^x = 1 + x + (x^2) / 2! + (x^3) / 3! + O (x^4)

And so from there i'm really not sure what comes next?? Could someone help me please??