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

\frac{d}{d x} (5 ln ∣ x - e^{x} ∣)

z \to 1 lim (\frac{z}{2 i})

\frac{d}{d x} (- \frac{3 x + 1}{x ^{2}})

4 (5 - 7 x)^{5}

x \cdot sin (π x)

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