Calculus 2 help! Macclaurin Series! Best answer awarded asap!?

Question

Find the Maclaurin series of the function f(x)=9x^3−2x^2−7x+2 (f(x)=∑n=0∞cnxn) c0= c1= c2= c3= c4= Find the radius of convergence R=

Answer 1

The Function f(x) = 9x³ - 2x³ - 7x + 2

The Maclaurin Series is given by

The Function is

f(x) = 9x³ - 2x²- 7x + 2

f(0) = 2

Differentiate f(x) with respect to x.

f'(x) = 27x² - 4x - 7

f'(0) = -7

Differentiate f'(x) with respect to x.

f''(x) = 54x - 4

f''(0) = - 4

Differentiate f''(x) with respect to x.

f'''(x) = 54x - 4

f'''(0) = 54

Differentiate f'''(x) with respect to x.

f''''(x) = 0

Therefore Maclaurin Series is

Now Maclaurin series is .

Therefore A0 = 2, A1 = -7, A2 = -2 and A3 = 9.

 the Radius of Convergence.

when the series is Convergent

=

=

= 4.5 x < 1

x < 2/9

Now radius of Convergence is -2/9 < x < 2/9

Therefore the radius of Convergence is -2/9 < x < 2/9.