What is taylor (cos(x))^2pi ?

The answer to taylor (cos(x))^2pi is pi-pix^2+pi/3 x^4-(2pi)/(45)x^6+pi/(315)x^8+\ldots

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taylor (cos(x))^2pi

taylor

(cos (x))^{2} π

π - π x^{2} + \frac{π}{3} x^{4} - \frac{2 π}{45} x^{6} + \frac{π}{315} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= π + \frac{0}{1 !} x + \frac{- 2 π}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{8 π}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 32 π}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{128 π}{8 !} x^{8} + \dots

Refine

= π - π x^{2} + \frac{π}{3} x^{4} - \frac{2 π}{45} x^{6} + \frac{π}{315} x^{8} + \dots

y^{^{'}} = \frac{x - 3}{y + 5}

\frac{d}{d x} (- 2 e^{4 x})

\int \frac{1}{5 ( 2 x - 1 )} d x

f (x) = x x

x \cdot cos (x), 1

What is taylor (cos(x))^2pi ?
The answer to taylor (cos(x))^2pi is pi-pix^2+pi/3 x^4-(2pi)/(45)x^6+pi/(315)x^8+\ldots