Question

Write out the first four terms of the Maclaurin series of f(x) if: f(0)=−5,f′(0)=−12,f′′(0)=15,f′′′(0)=−10

Answer 1

do you know the formula for a Mclaurin series?

Answer 2

T(x)=sum of (f^(n)(c)(x-c)^n)/(n!)

Answer 3

n ranges from 0 to infinity. But this case, n ranges from 0 to 3

Answer 4

so you have f^0(0)x/0! + f'(0)x / 1! + f''(0) x^2 / 2! + f'''(0) x^3 / 3!

you're already given the values of derivative at 0. Plug and chug

Answer 5

typo should beso you have f^0(0)/0! + f'(0)x / 1! + f''(0) x^2 / 2! + f'''(0) x^3 / 3!

and note: f^0(0) means f(0)

Answer 6

Thank you!!!