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Popular Calculus >

taylor e^{1/(x-9)},7

Solution

taylor

e^{\frac{1}{x - 9}}, 7

Solution

\frac{1}{e ^{\frac{1}{2}}} - \frac{1}{4 e ^{\frac{1}{2}}} (x - 7) - \frac{3}{32 e ^{\frac{1}{2}}} (x - 7)^{2} - \frac{13}{384 e ^{\frac{1}{2}}} (x - 7)^{3} - \frac{71}{6144 e ^{\frac{1}{2}}} (x - 7)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{e ^{\frac{1}{2}}} + \frac{\frac{d}{d x} ( e ^{\frac{1}{x - 9}} ) ( 7 )}{1 !} (x - 7) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{\frac{1}{x - 9}} ) ( 7 )}{2 !} (x - 7)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{\frac{1}{x - 9}} ) ( 7 )}{3 !} (x - 7)^{3} + \dots

Evaluate Derivatives

= \frac{1}{e ^{\frac{1}{2}}} + \frac{- \frac{1}{4 e ^{\frac{1}{2}}}}{1 !} (x - 7) + \frac{- \frac{3}{16 e ^{\frac{1}{2}}}}{2 !} (x - 7)^{2} + \frac{- \frac{13}{64 e ^{\frac{1}{2}}}}{3 !} (x - 7)^{3} + \frac{- \frac{71}{256 e ^{\frac{1}{2}}}}{4 !} (x - 7)^{4} + \dots

Refine

= \frac{1}{e ^{\frac{1}{2}}} - \frac{1}{4 e ^{\frac{1}{2}}} (x - 7) - \frac{3}{32 e ^{\frac{1}{2}}} (x - 7)^{2} - \frac{13}{384 e ^{\frac{1}{2}}} (x - 7)^{3} - \frac{71}{6144 e ^{\frac{1}{2}}} (x - 7)^{4} + \dots

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