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

The answer to taylor cos(x)+sin(x) is 1+x-1/2 x^2-1/6 x^3+1/24 x^4+\ldots

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taylor cos(x)+sin(x)

taylor

cos (x) + sin (x)

1 + x - \frac{1}{2} x^{2} - \frac{1}{6} x^{3} + \frac{1}{24} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 + x - \frac{1}{2} x^{2} - \frac{1}{6} x^{3} + \frac{1}{24} x^{4} + \dots

\frac{\partial}{\partial x} (- 2 y cos (x))

tan (9 x)

\int e^{2 x} sin (2 x) d x

\frac{d}{d x} y + y x^{7} = 0

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

What is taylor cos(x)+sin(x) ?
The answer to taylor cos(x)+sin(x) is 1+x-1/2 x^2-1/6 x^3+1/24 x^4+\ldots