How do i do this calc problem? Use a third degree Taylor polynomial to approximate the number e.?

Answer 1

Use the function f(x) = e^x.
Find the Taylor polynomial of this function about x = 0. Then evaluate the Taylor polynomial at x = 1 to estimate e.

Answer 2

Use the Taylor series for e^x: e^x=1 + x + x^2/2! + x^3/3! + ...
Since you're using a third degree Taylor polynomial, go up to the x^3 term.
Substitute 1 (the exponent for e) in for x: e=1 + 1 + 1^2/2! +1^3/3!
e=2.667

Answer 3

e=1+1+1/2!+1/3! This is the Mac Laurin series which is the Taylor series at x=0
e=2.5 +0.1667 =2.6667 with four terms