taylor e^{-x},-0.75

Lösung

taylor

e^{- x}, - 0.75

2.11700 \dots - 2.11700 \dots (x + 0.75) + 1.05850 \dots (x + 0.75)^{2} - 0.35283 \dots (x + 0.75)^{3} + 0.08820 \dots (x + 0.75)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 2.11700 \dots + \frac{\frac{d}{d x} ( e ^{- x} ) ( - 0.75 )}{1 !} (x + 0.75) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- x} ) ( - 0.75 )}{2 !} (x + 0.75)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- x} ) ( - 0.75 )}{3 !} (x + 0.75)^{3} + \dots

Evaluate Derivatives

= 2.11700 \dots + \frac{- 2.11700 \dots}{1 !} (x + 0.75) + \frac{2.11700 \dots}{2 !} (x + 0.75)^{2} + \frac{- 2.11700 \dots}{3 !} (x + 0.75)^{3} + \frac{2.11700 \dots}{4 !} (x + 0.75)^{4} + \dots

Fasse zusammen

= 2.11700 \dots - 2.11700 \dots (x + 0.75) + 1.05850 \dots (x + 0.75)^{2} - 0.35283 \dots (x + 0.75)^{3} + 0.08820 \dots (x + 0.75)^{4} + \dots

f^{^{''}} (x) = x

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