Answer to Question #251065 in Calculus for angel

Question #251065

Write the first four terms of a Maclaurin series for ๐‘“(๐‘ฅ)= ๐‘’๐‘ฅ


1
Expert's answer
2021-10-14T15:24:02-0400

"f(x) = {e^x} \\Rightarrow f'(x) = {e^x} \\Rightarrow f''(x) = {e^x} \\Rightarrow f'''(x) = {e^x}"

Then

"f(x) = f(0) + \\frac{{f'(0)}}{{1!}}x + \\frac{{f''(0)}}{{2!}}{x^2} + \\frac{{f'''(0)}}{{3!}}{x^3} + ... = {e^0} + \\frac{{{e^0}}}{1}x + \\frac{{{e^0}}}{2}{x^2} + \\frac{{{e^0}}}{6}{x^3} + ... = 1 + x + \\frac{1}{2}{x^2} + \\frac{1}{6}{x^3} + ..."

Answer: "f(x) = 1 + x + \\frac{1}{2}{x^2} + \\frac{1}{6}{x^3} + ..."


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