What is taylor sin(3x) ?

The answer to taylor sin(3x) is 3x-9/2 x^3+81/40 x^5-243/560 x^7+243/4480 x^9+\ldots

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taylor sin(3x)

taylor

sin (3 x)

3 x - \frac{9}{2} x^{3} + \frac{81}{40} x^{5} - \frac{243}{560} x^{7} + \frac{243}{4480} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 3 x - \frac{9}{2} x^{3} + \frac{81}{40} x^{5} - \frac{243}{560} x^{7} + \frac{243}{4480} x^{9} + \dots

\int 4 e^{c o s (x)} sin (x) d x

\int \frac{2 sin ( x )}{cos ( x )} d x

f (x) = tan (8 x)

\int \frac{1}{( x ^{2} + 4 ) ( x + 2 )} d x

t \to 0 lim (tan (7 t))

What is taylor sin(3x) ?
The answer to taylor sin(3x) is 3x-9/2 x^3+81/40 x^5-243/560 x^7+243/4480 x^9+\ldots