Question

Write out the first four terms of the maclaurin series of f(x) if f(0)=7,f′(0)=3,f′′(0)=13,f′′′(0)=12

Answer 1

The general from for a maclaurin series is the nth derivative times x to the nth power divided by n factorial:
$\frac{f(0)}{0!}x^{0}+ \frac{f'(0)}{1!}x^{1}+ \frac{f''(0)}{2!}x^{2}+ \frac{f'''(0)}{3!}x^{3} \\ \\ 7+ 3x+ \frac{13}{2}x^{2}+ 2x^{3}$