What is the taylor series of 6e^(-x/9) at x = 0?

Answer 1

f(x) = 6e^-x/9 f(0) = 6

f'(x) = -6e^-x/9/9 f'(0) = -6/9

f"(x) = 6e^-x/9/9² f"(0) = 6/9²

f'''(x) = 6e^-x/9/9³ f'''(0) = 6/9³

:

f(x) = 6-6/9x+6x²/(9²2!)-6x³/(9³3!)+-........

∞

f(x) = 6∑(-1)ⁿxⁿ/(9ⁿn!)

n=0