What is taylor xcos(x) ?

The answer to taylor xcos(x) is x-1/2 x^3+1/24 x^5-1/720 x^7+1/40320 x^9+\ldots

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taylor xcos(x)

taylor

x cos (x)

x - \frac{1}{2} x^{3} + \frac{1}{24} x^{5} - \frac{1}{720} x^{7} + \frac{1}{40320} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= x - \frac{1}{2} x^{3} + \frac{1}{24} x^{5} - \frac{1}{720} x^{7} + \frac{1}{40320} x^{9} + \dots

\int \frac{2 + x}{4 x ^{2} - 4 x - 3} d x

f (x) = ln (x - 1)

\int (12 x^{2} - 8 x + 2) d x

\frac{d y}{d x} = \frac{( x - 1 )}{y}

\frac{d}{d x} (7 arcsin (x^{2}))

What is taylor xcos(x) ?
The answer to taylor xcos(x) is x-1/2 x^3+1/24 x^5-1/720 x^7+1/40320 x^9+\ldots