What is taylor cos(x/2) ?

The answer to taylor cos(x/2) is 1-1/8 x^2+1/384 x^4-1/46080 x^6+1/10321920 x^8+\ldots

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taylor cos(x/2)

taylor

cos (\frac{x}{2})

1 - \frac{1}{8} x^{2} + \frac{1}{384} x^{4} - \frac{1}{46080} x^{6} + \frac{1}{10321920} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- \frac{1}{4}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{1}{16}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{1}{64}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{1}{256}}{8 !} x^{8} + \dots

Refine

= 1 - \frac{1}{8} x^{2} + \frac{1}{384} x^{4} - \frac{1}{46080} x^{6} + \frac{1}{10321920} x^{8} + \dots

\int \frac{1}{e ^{5 x}} d x

\int - 7 x^{- 8} d x

y = 5 csc (x) + 7 cos (x)

\int \frac{x ^{2} - 10 x + 4}{x ^{3}} d x

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

What is taylor cos(x/2) ?
The answer to taylor cos(x/2) is 1-1/8 x^2+1/384 x^4-1/46080 x^6+1/10321920 x^8+\ldots