taylor e^x,5

Lösung

taylor

e^{x}, 5

e^{5} + e^{5} (x - 5) + \frac{e ^{5}}{2} (x - 5)^{2} + \frac{e ^{5}}{6} (x - 5)^{3} + \frac{e ^{5}}{24} (x - 5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= e^{5} + \frac{\frac{d}{d x} ( e ^{x} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{x} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= e^{5} + \frac{e ^{5}}{1 !} (x - 5) + \frac{e ^{5}}{2 !} (x - 5)^{2} + \frac{e ^{5}}{3 !} (x - 5)^{3} + \frac{e ^{5}}{4 !} (x - 5)^{4} + \dots

Fasse zusammen

= e^{5} + e^{5} (x - 5) + \frac{e ^{5}}{2} (x - 5)^{2} + \frac{e ^{5}}{6} (x - 5)^{3} + \frac{e ^{5}}{24} (x - 5)^{4} + \dots

t an g e n t f (x) = \frac{5}{x}, at x = - \frac{1}{5}

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