What is taylor 3sin(-x) ?

The answer to taylor 3sin(-x) is -3x+1/2 x^3-1/40 x^5+1/1680 x^7-1/120960 x^9+\ldots

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taylor 3sin(-x)

taylor

3 sin (- x)

- 3 x + \frac{1}{2} x^{3} - \frac{1}{40} x^{5} + \frac{1}{1680} x^{7} - \frac{1}{120960} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= - 3 x + \frac{1}{2} x^{3} - \frac{1}{40} x^{5} + \frac{1}{1680} x^{7} - \frac{1}{120960} x^{9} + \dots

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

y = (x + \frac{1}{x})^{5}

x \to 0 lim (x - 3)

\frac{\partial}{\partial y} (arctan (x + 4 y))

x \to 4 lim (3 x^{2})

What is taylor 3sin(-x) ?
The answer to taylor 3sin(-x) is -3x+1/2 x^3-1/40 x^5+1/1680 x^7-1/120960 x^9+\ldots