Find the Maclaurin series expansion of f(x) = ex at x = 0. | Mathematics I 2080

Mathematics I20805 marksTaylor's and Maclaurin's series

Find the Maclaurin series expansion of $f(x) = e^x$ at $x = 0$ . [5]

Find the Maclaurin series expansion of $f(x) = e^x$ at $x = 0$. [5]

The Maclaurin series is a special case of the Taylor series expanded about x = 0. It is given by: $f(x) = f(0) + f'(0)\cdot x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + \cdots = \sum{n=0}^{\infty} \frac{f^{(n)}(0)}{n!}x^n$ --- Since the derivative of eˣ is eˣ itself: Derivative Expression...

The Maclaurin series is a special case of the Taylor series expanded about x = 0. It is given by: $$f(x) = f(0) + f'(0)\cdot x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + \cdots = \sum{n=0}^{\infty} \frac{f^{(n)}(0)}{n!}x^n$$ --- Since the derivative of eˣ is eˣ itself: Derivative Expression...

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