What is taylor x^{-2},4 ?

The answer to taylor x^{-2},4 is 1/16-1/32 (x-4)+3/256 (x-4)^2-1/256 (x-4)^3+5/4096 (x-4)^4+\ldots

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taylor x^{-2},4

taylor

x^{- 2}, 4

\frac{1}{16} - \frac{1}{32} (x - 4) + \frac{3}{256} (x - 4)^{2} - \frac{1}{256} (x - 4)^{3} + \frac{5}{4096} (x - 4)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{16} + \frac{\frac{d}{d x} ( x ^{- 2} ) ( 4 )}{1 !} (x - 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{- 2} ) ( 4 )}{2 !} (x - 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{- 2} ) ( 4 )}{3 !} (x - 4)^{3} + \dots

Evaluate Derivatives

= \frac{1}{16} + \frac{- \frac{1}{32}}{1 !} (x - 4) + \frac{\frac{3}{128}}{2 !} (x - 4)^{2} + \frac{- \frac{3}{128}}{3 !} (x - 4)^{3} + \frac{\frac{15}{512}}{4 !} (x - 4)^{4} + \dots

Refine

= \frac{1}{16} - \frac{1}{32} (x - 4) + \frac{3}{256} (x - 4)^{2} - \frac{1}{256} (x - 4)^{3} + \frac{5}{4096} (x - 4)^{4} + \dots

\int \frac{5}{4 x} d x

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What is taylor x^{-2},4 ?
The answer to taylor x^{-2},4 is 1/16-1/32 (x-4)+3/256 (x-4)^2-1/256 (x-4)^3+5/4096 (x-4)^4+\ldots