Another taylor series problem?

Question

obtain the taylor polynomial of degree 3 for e^(2x) about x=1

then approximate e^1.8 up to 4 decimal places.

Answer 1

f(x) = e^(2x) . . . .. . .  f(1) = e

f'(x) = 2e^(2x) .. . .. . f'(1) = 2e

f''(x) = 4e^(2x) ... .... f''(1) = 4e

f'''(x) = 8e^(2x) .. . .. .f'''(1) = 8e

then

e^(2x) ≈ e + 2e(x - 1) + (4e)(x-1)^2 / 2 + (8e) (x-1)^3 / 6

then x = 1.8

you still need calculator because there is the number e.