What is maclaurin 9sin(3x) ?

The answer to maclaurin 9sin(3x) is 27x-81/2 x^3+729/40 x^5-2187/560 x^7+2187/4480 x^9+\ldots

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maclaurin 9sin(3x)

maclaurin

9 sin (3 x)

27 x - \frac{81}{2} x^{3} + \frac{729}{40} x^{5} - \frac{2187}{560} x^{7} + \frac{2187}{4480} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( 9 sin ( 3 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 9 sin ( 3 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 9 sin ( 3 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{27}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 243}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{2187}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 19683}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{177147}{9 !} x^{9} + \dots

Refine

= 27 x - \frac{81}{2} x^{3} + \frac{729}{40} x^{5} - \frac{2187}{560} x^{7} + \frac{2187}{4480} x^{9} + \dots

\int 1 - 49 x^{2} d x

\int_{0}^{9} 2 x - \frac{2 x}{3} d x

S (t) = \frac{60 t ^{2}}{t ^{2} + 150}

x x^{2} + 60 (2.9)

f (x) = e^{10 x}

What is maclaurin 9sin(3x) ?
The answer to maclaurin 9sin(3x) is 27x-81/2 x^3+729/40 x^5-2187/560 x^7+2187/4480 x^9+\ldots