maclaurin sin(5x)*sin(4x)

Lösung

maclaurin

sin (5 x) \cdot sin (4 x)

20 x^{2} - \frac{410}{3} x^{4} + \frac{6643}{18} x^{6} - \frac{134521}{252} x^{8} + \frac{8716961}{18144} x^{10} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( sin ( 5 x ) sin ( 4 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( 5 x ) sin ( 4 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( 5 x ) sin ( 4 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{40}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 3280}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{265720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 21523360}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{1743392200}{10 !} x^{10} + \dots

Fasse zusammen

= 20 x^{2} - \frac{410}{3} x^{4} + \frac{6643}{18} x^{6} - \frac{134521}{252} x^{8} + \frac{8716961}{18144} x^{10} + \dots

\int (x^{2} + x)^{12} (2 x + 1) d x

\int \frac{1}{2} sin (2 x) - cos (x) + C d x

z \to - 2 lim (z^{3} + 8)

t an g e n t f (x) = \frac{8}{x}, at x = 25

x \to 0 lim (1 - 1 + x)