What is maclaurin xsin(-2x),\at pi ?

The answer to maclaurin xsin(-2x),\at pi is -2x^2+4/3 x^4-4/15 x^6+8/315 x^8-4/2835 x^{10}+\ldots

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maclaurin xsin(-2x),\at pi

maclaurin

x sin (- 2 x), at π

- 2 x^{2} + \frac{4}{3} x^{4} - \frac{4}{15} x^{6} + \frac{8}{315} x^{8} - \frac{4}{2835} x^{10} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{- 4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{32}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 192}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1024}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{- 5120}{10 !} x^{10} + \dots

Refine

= - 2 x^{2} + \frac{4}{3} x^{4} - \frac{4}{15} x^{6} + \frac{8}{315} x^{8} - \frac{4}{2835} x^{10} + \dots

x \to 0 lim (\frac{x}{x ^{2} + 6 x})

\int t + 8 d t

\int x^{3} + x^{2} d x

\frac{d}{d x} (4 - x^{2} + y^{2})

\int (\frac{12 x ^{4} + 3 x ^{2} + 6 a x}{2 x}) d x

What is maclaurin xsin(-2x),\at pi ?
The answer to maclaurin xsin(-2x),\at pi is -2x^2+4/3 x^4-4/15 x^6+8/315 x^8-4/2835 x^{10}+\ldots