What is taylor x-sin(x) ?

The answer to taylor x-sin(x) is 1/6 x^3-1/120 x^5+1/5040 x^7-1/362880 x^9+\ldots

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taylor x-sin(x)

taylor

x - sin (x)

\frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \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{0}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 1}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{1}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 1}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

f (θ) = 4 cos (θ)

\int 4 x e^{\frac{2}{3} x} d x

x \to - 16 lim (x + 16 - 4)

y^{^{''}} - 3 y^{^{'}} - 18 y = 0, y (0) = 1, y^{^{'}} (0) = - 2

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

What is taylor x-sin(x) ?
The answer to taylor x-sin(x) is 1/6 x^3-1/120 x^5+1/5040 x^7-1/362880 x^9+\ldots