What is taylor cos(y) ?

The answer to taylor cos(y) is sum from n=0 to infinity}(-1)^n(x^{2n of)/((2n)!)

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taylor cos(y)

taylor

cos (y)

n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n}}{( 2 n ) !}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 - \frac{1}{2 !} y^{2} + \frac{1}{4 !} y^{4} - \frac{1}{6 !} y^{6} + \frac{1}{8 !} y^{8} + \dots

The series sum representation

= n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n}}{( 2 n ) !}

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What is taylor cos(y) ?
The answer to taylor cos(y) is sum from n=0 to infinity}(-1)^n(x^{2n of)/((2n)!)