What is taylor x^{-2},5 ?

The answer to taylor x^{-2},5 is 1/25-2/125 (x-5)+3/625 (x-5)^2-4/3125 (x-5)^3+1/3125 (x-5)^4+\ldots

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taylor x^{-2},5

taylor

x^{- 2}, 5

\frac{1}{25} - \frac{2}{125} (x - 5) + \frac{3}{625} (x - 5)^{2} - \frac{4}{3125} (x - 5)^{3} + \frac{1}{3125} (x - 5)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{25} + \frac{\frac{d}{d x} ( x ^{- 2} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{- 2} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{- 2} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= \frac{1}{25} + \frac{- \frac{2}{125}}{1 !} (x - 5) + \frac{\frac{6}{625}}{2 !} (x - 5)^{2} + \frac{- \frac{24}{3125}}{3 !} (x - 5)^{3} + \frac{\frac{24}{3125}}{4 !} (x - 5)^{4} + \dots

Refine

= \frac{1}{25} - \frac{2}{125} (x - 5) + \frac{3}{625} (x - 5)^{2} - \frac{4}{3125} (x - 5)^{3} + \frac{1}{3125} (x - 5)^{4} + \dots

\frac{d}{d x} (sin (x^{12}))

x \to 0 lim (\frac{- 1}{x})

x^{2} sin (x) tan (x)

\int (3 x + 1) (2 - x) d x

y = x^{3}, (- 1, - 1)

What is taylor x^{-2},5 ?
The answer to taylor x^{-2},5 is 1/25-2/125 (x-5)+3/625 (x-5)^2-4/3125 (x-5)^3+1/3125 (x-5)^4+\ldots