What is taylor cos(x),x=0 ?

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

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taylor cos(x),x=0

taylor

cos (x), x = 0

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

The series sum representation

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

t \to 0 lim (\frac{1}{t})

x \to 7 - lim (e^{\frac{3}{7 - x}})

\frac{d}{d x} (\frac{2 - ln ( x )}{2 x x})

cos (2 π t)

t^{2} y^{^{''}} - 6 t y^{^{'}} + 10 y = 0

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