What is taylor sin(x)pi ?

The answer to taylor sin(x)pi is pix-pi/6 x^3+pi/(120)x^5-pi/(5040)x^7+pi/(362880)x^9+\ldots

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taylor sin(x)pi

taylor

sin (x) π

π x - \frac{π}{6} x^{3} + \frac{π}{120} x^{5} - \frac{π}{5040} x^{7} + \frac{π}{362880} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= π x - \frac{π}{6} x^{3} + \frac{π}{120} x^{5} - \frac{π}{5040} x^{7} + \frac{π}{362880} x^{9} + \dots

\int \frac{6 ln ^{2} ( x )}{x} d x

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

ln (\frac{1 + x}{1 - x}), 0

y^{^{'}} + x y^{2} = 0

x \to 0 lim (x + a)

What is taylor sin(x)pi ?
The answer to taylor sin(x)pi is pix-pi/6 x^3+pi/(120)x^5-pi/(5040)x^7+pi/(362880)x^9+\ldots