What is taylor sin(x)-x ?

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

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taylor sin(x)-x

taylor

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

y^{^{''}} + 4 y = 20 sin (2 t)

f (x) = \frac{5 x}{x + 3}, (2, 2)

13.375 ln (\frac{x}{x - 1250})

\int 6 x (1 - x) d x

t^{2} \cdot y^{^{'}} + t y = 7, y (1) = 7

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