What is taylor cos(x) pi/2 ?

The answer to taylor cos(x) pi/2 is pi/2-pi/4 x^2+pi/(48)x^4-pi/(1440)x^6+pi/(80640)x^8+\ldots

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taylor cos(x) pi/2

taylor

cos (x) \frac{π}{2}

\frac{π}{2} - \frac{π}{4} x^{2} + \frac{π}{48} x^{4} - \frac{π}{1440} x^{6} + \frac{π}{80640} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= \frac{π}{2} - \frac{π}{4} x^{2} + \frac{π}{48} x^{4} - \frac{π}{1440} x^{6} + \frac{π}{80640} x^{8} + \dots

y^{^{'}} = a y + b

\int_{0}^{\frac{1}{2}} \frac{4}{1 + 4 x ^{2}} d x

\int \frac{1}{2 ( x ^{2} + 1 )} d x

\int \frac{1}{x ^{2}} x^{'} d x

(5 x - 3) y^{^{''}} + y^{^{'}} = 0

What is taylor cos(x) pi/2 ?
The answer to taylor cos(x) pi/2 is pi/2-pi/4 x^2+pi/(48)x^4-pi/(1440)x^6+pi/(80640)x^8+\ldots