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Popular Calculus >

taylor 1/(x^2),\at 4

Solution

taylor

\frac{1}{x ^{2}}, at 4

Solution

\frac{- \frac{2}{( at 4 ) ^{3}}}{1 !} (x - at 4) + \frac{\frac{6}{( at 4 ) ^{4}}}{2 !} (x - at 4)^{2} + \frac{- \frac{24}{( at 4 ) ^{5}}}{3 !} (x - at 4)^{3} + \frac{\frac{120}{( at 4 ) ^{6}}}{4 !} (x - at 4)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{( at 4 ) ^{2}} + \frac{- \frac{2}{( at 4 ) ^{3}}}{1 !} (x - at 4) + \frac{\frac{6}{( at 4 ) ^{4}}}{2 !} (x - at 4)^{2} + \frac{- \frac{24}{( at 4 ) ^{5}}}{3 !} (x - at 4)^{3} + \frac{\frac{120}{( at 4 ) ^{6}}}{4 !} (x - at 4)^{4} + \dots

Refine

= \frac{- \frac{2}{( at 4 ) ^{3}}}{1 !} (x - at 4) + \frac{\frac{6}{( at 4 ) ^{4}}}{2 !} (x - at 4)^{2} + \frac{- \frac{24}{( at 4 ) ^{5}}}{3 !} (x - at 4)^{3} + \frac{\frac{120}{( at 4 ) ^{6}}}{4 !} (x - at 4)^{4} + \dots

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Frequently Asked Questions (FAQ)

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