What is taylor x*sin(x) ?

The answer to taylor x*sin(x) is x^2-1/6 x^4+1/120 x^6-1/5040 x^8+1/362880 x^{10}+\ldots

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taylor x*sin(x)

taylor

x \cdot sin (x)

x^{2} - \frac{1}{6} x^{4} + \frac{1}{120} x^{6} - \frac{1}{5040} x^{8} + \frac{1}{362880} x^{10} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= x^{2} - \frac{1}{6} x^{4} + \frac{1}{120} x^{6} - \frac{1}{5040} x^{8} + \frac{1}{362880} x^{10} + \dots

\int \frac{3 ( - 5 + ln ( 4 x ) ) ^{3}}{x} d x

f (x) = x^{2} - 9 x + 18, 4, at x = 3

\frac{d}{d x} (\frac{x}{( 3 x - 8 ) ^{8}})

\frac{4 s}{s ^{2} + 16}

f (x) = \frac{3}{x + 3}, at x = - \frac{1}{3}

What is taylor x*sin(x) ?
The answer to taylor x*sin(x) is x^2-1/6 x^4+1/120 x^6-1/5040 x^8+1/362880 x^{10}+\ldots