maclaurin ((e^x-e^{-x}))/2

Lösung

maclaurin

\frac{( e ^{x} - e ^{- x} )}{2}

x + \frac{1}{6} x^{3} + \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} + \frac{1}{362880} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

= x + \frac{1}{6} x^{3} + \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} + \frac{1}{362880} x^{9} + \dots

t an g e n t \frac{4}{x}

t an g e n t y = x, at x = 81

f^{^{'}} (x) = x 7 - x^{2}

x \to 3 lim (77)

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