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Popular Calculus >

taylor 1/(2x),\at 2

Solution

taylor

\frac{1}{2 x}, at 2

Solution

\frac{- \frac{1}{2 ( at 2 ) ^{2}}}{1 !} (x - at 2) + \frac{\frac{1}{( at 2 ) ^{3}}}{2 !} (x - at 2)^{2} + \frac{- \frac{3}{( at 2 ) ^{4}}}{3 !} (x - at 2)^{3} + \frac{\frac{12}{( at 2 ) ^{5}}}{4 !} (x - at 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{2 at 2} + \frac{- \frac{1}{2 ( at 2 ) ^{2}}}{1 !} (x - at 2) + \frac{\frac{1}{( at 2 ) ^{3}}}{2 !} (x - at 2)^{2} + \frac{- \frac{3}{( at 2 ) ^{4}}}{3 !} (x - at 2)^{3} + \frac{\frac{12}{( at 2 ) ^{5}}}{4 !} (x - at 2)^{4} + \dots

Refine

= \frac{- \frac{1}{2 ( at 2 ) ^{2}}}{1 !} (x - at 2) + \frac{\frac{1}{( at 2 ) ^{3}}}{2 !} (x - at 2)^{2} + \frac{- \frac{3}{( at 2 ) ^{4}}}{3 !} (x - at 2)^{3} + \frac{\frac{12}{( at 2 ) ^{5}}}{4 !} (x - at 2)^{4} + \dots

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Frequently Asked Questions (FAQ)

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