Find the Taylor series at x = 0 of f(x) = $e ^ { 3 x }$ by computing four derivatives and using the definition of the Taylor series. Is $1 - 3 x + \frac { 3 ^ { 2 } } { 2 ! } x ^ { 2 } - \frac { 3 ^ { 3 } } { 3 ! } x ^ { 3 } + \frac { 3 ^ { 4 } } { 4 ! } x ^ { 4 } - \ldots$ the correct answer?

Question

Find the Taylor series at x = 0 of f(x) =

e ^ { 3 x }

by computing four derivatives and using the definition of the Taylor series. Is

1 - 3 x + \frac { 3 ^ { 2 } } { 2 ! } x ^ { 2 } - \frac { 3 ^ { 3 } } { 3 ! } x ^ { 3 } + \frac { 3 ^ { 4 } } { 4 ! } x ^ { 4 } - \ldots

the correct answer?

Quizplus · Accepted Answer

The correct Taylor series for $f(x) = e^{3x}$ at $x = 0$ is $1 + 3x + \frac{3^2}{2!}x^2 + \frac{3^3}{3!}x^3 + \frac{3^4}{4!}x^4 + \ldots$. The given series incorrectly alternates signs.

Find the Taylor Series at X = 0 of F(x) e3xe ^ { 3 x }e3x

Find the Taylor Series at X = 0 of F(x) $e ^ { 3 x }$