What is taylor x-1-0.5sin(x) ?

The answer to taylor x-1-0.5sin(x) is -1+0.5x+0.08333…x^3-0.00416…x^5+0.00009…x^7+\ldots

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taylor x-1-0.5sin(x)

taylor

x - 1 - 0.5 sin (x)

- 1 + 0.5 x + 0.08333 \dots x^{3} - 0.00416 \dots x^{5} + 0.00009 \dots x^{7} + \dots

Solution steps

Apply the Taylor Formula

= - 1 + \frac{\frac{d}{d x} ( x - 1 - 0.5 sin ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x - 1 - 0.5 sin ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x - 1 - 0.5 sin ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= - 1 + \frac{0.5}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0.5}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 0.5}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0.5}{7 !} x^{7} + \dots

Refine

= - 1 + 0.5 x + 0.08333 \dots x^{3} - 0.00416 \dots x^{5} + 0.00009 \dots x^{7} + \dots

\int_{8}^{- 1} x^{2} - 8 d x

y^{^{'}} - \frac{6 y}{x} = \frac{y ^{4}}{x ^{12}}

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

\int \frac{1 - 2 x ^{5}}{x} d x

\int_{0}^{1} (1 - x^{2})^{\frac{3}{2}} d x

What is taylor x-1-0.5sin(x) ?
The answer to taylor x-1-0.5sin(x) is -1+0.5x+0.08333…x^3-0.00416…x^5+0.00009…x^7+\ldots