What is taylor 10sin(3x) ?

The answer to taylor 10sin(3x) is 30x-45x^3+81/4 x^5-243/56 x^7+243/448 x^9+\ldots

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taylor 10sin(3x)

taylor

10 sin (3 x)

30 x - 45 x^{3} + \frac{81}{4} x^{5} - \frac{243}{56} x^{7} + \frac{243}{448} x^{9} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 10 sin ( 3 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 10 sin ( 3 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 10 sin ( 3 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{30}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 270}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{2430}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 21870}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{196830}{9 !} x^{9} + \dots

Refine

= 30 x - 45 x^{3} + \frac{81}{4} x^{5} - \frac{243}{56} x^{7} + \frac{243}{448} x^{9} + \dots

\frac{d y}{d x}, \frac{x}{y} = 9

\frac{d y}{d x} = y sin (x)

\int \frac{e ^{2 x}}{2 + e ^{2 x}} d x

\int tan^{4} (x) sec^{4} (x) d x

\int x^{2} + 2 y d y

What is taylor 10sin(3x) ?
The answer to taylor 10sin(3x) is 30x-45x^3+81/4 x^5-243/56 x^7+243/448 x^9+\ldots