taylor pi/6 cos(x)

Soluzione

taylor

\frac{π}{6} cos (x)

\frac{π}{6} - \frac{π}{12} x^{2} + \frac{π}{144} x^{4} - \frac{π}{4320} x^{6} + \frac{π}{241920} x^{8} + \dots

Fasi della soluzione

Applica la Formula di Taylor

= \frac{π}{6} + \frac{\frac{d}{d x} ( \frac{π}{6} cos ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{π}{6} cos ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{π}{6} cos ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Valuta derivate

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

Affinare

= \frac{π}{6} - \frac{π}{12} x^{2} + \frac{π}{144} x^{4} - \frac{π}{4320} x^{6} + \frac{π}{241920} x^{8} + \dots

d er i v a t i v e 2 - x^{6}

\int 5 x - x^{2} - x d x

h \to 0 lim (\frac{( 4 + h ) - ( 4 )}{h})

x \frac{d y}{d x} - 2 y = x^{- 2} + 2 x^{3} e^{x}

\int \frac{e ^{x}}{5 + e ^{2 x}} d x