taylor sin(x pi/2)

Lösung

taylor

sin (x \frac{π}{2})

\frac{π}{2} x - \frac{π ^{3}}{48} x^{3} + \frac{π ^{5}}{3840} x^{5} - \frac{π ^{7}}{645120} x^{7} + \frac{π ^{9}}{185794560} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{\frac{π}{2}}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- \frac{π ^{3}}{8}}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{\frac{π ^{5}}{32}}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- \frac{π ^{7}}{128}}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{\frac{π ^{9}}{512}}{9 !} x^{9} + \dots

Fasse zusammen

= \frac{π}{2} x - \frac{π ^{3}}{48} x^{3} + \frac{π ^{5}}{3840} x^{5} - \frac{π ^{7}}{645120} x^{7} + \frac{π ^{9}}{185794560} x^{9} + \dots

\int e^{x} \cdot x^{3} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}

x \to - 2 lim (\frac{3 x - 6 - 2}{x ^{3} + 8})

\int ln (x) \frac{1}{x} d x

d er i v a t i v e (5 x^{6} + 4 x^{3})^{4}