Question

Write the Maclaurin series for f(x)= e^x. I do not understand why its first term is "1".

Answer 1

f(x) = e^x
f' (x) = e^x
f^n (x) = e^x no matter how often you differentiate it, it is still e^x
and the formula an = f^n (x) / n/ = where x equals zero
f^n (0 ) / n/ = e^0 / n! = 1 /n!
and a1 = f (0 ) = 1

Maclaurin series of f(x) = e^x = 1 + x + x²/2/ + x³/3/ + ...
( / means factorial)

Answer 2

I was confused as to why 0! =1. I should remember it like an exponent: 8^0 = 1. I understand now, thanks

Answer 3

0! by definition is 1

Answer 4

yea i totally understand your confusion. 0! is 1 , anything to the power of 0 is also 1

Answer 5

Thanks guys! There may be more questions about Maclaurin