What is taylor cos(2x)+sin(x) ?

The answer to taylor cos(2x)+sin(x) is 1+x-2x^2-1/6 x^3+2/3 x^4+\ldots

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taylor cos(2x)+sin(x)

taylor

cos (2 x) + sin (x)

1 + x - 2 x^{2} - \frac{1}{6} x^{3} + \frac{2}{3} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{- 4}{2 !} x^{2} + \frac{- 1}{3 !} x^{3} + \frac{16}{4 !} x^{4} + \dots

Refine

= 1 + x - 2 x^{2} - \frac{1}{6} x^{3} + \frac{2}{3} x^{4} + \dots

y^{^{''}} - 6 y^{^{'}} + 9 y = 0

\int_{0}^{L} x d x

y^{^{'}} + 4 y = x^{2}

\int_{- 21}^{0} \frac{1}{4 - x} d x

What is taylor cos(2x)+sin(x) ?
The answer to taylor cos(2x)+sin(x) is 1+x-2x^2-1/6 x^3+2/3 x^4+\ldots