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Popular >

taylor ln(x/2),\at 2

Solution

taylor

ln (\frac{x}{2}), at 2

Solution

\frac{\frac{1}{at 2}}{1 !} (x - at 2) + \frac{- \frac{1}{( at 2 ) ^{2}}}{2 !} (x - at 2)^{2} + \frac{\frac{2}{( at 2 ) ^{3}}}{3 !} (x - at 2)^{3} + \frac{- \frac{6}{( at 2 ) ^{4}}}{4 !} (x - at 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= ln (\frac{at 2}{2}) + \frac{\frac{1}{at 2}}{1 !} (x - at 2) + \frac{- \frac{1}{( at 2 ) ^{2}}}{2 !} (x - at 2)^{2} + \frac{\frac{2}{( at 2 ) ^{3}}}{3 !} (x - at 2)^{3} + \frac{- \frac{6}{( at 2 ) ^{4}}}{4 !} (x - at 2)^{4} + \dots

Refine

= \frac{\frac{1}{at 2}}{1 !} (x - at 2) + \frac{- \frac{1}{( at 2 ) ^{2}}}{2 !} (x - at 2)^{2} + \frac{\frac{2}{( at 2 ) ^{3}}}{3 !} (x - at 2)^{3} + \frac{- \frac{6}{( at 2 ) ^{4}}}{4 !} (x - at 2)^{4} + \dots

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