What is taylor 2/(x^2),2 ?

The answer to taylor 2/(x^2),2 is 1/2-1/2 (x-2)+3/8 (x-2)^2-1/4 (x-2)^3+5/32 (x-2)^4+\ldots

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taylor 2/(x^2),2

taylor

\frac{2}{x ^{2}}, 2

\frac{1}{2} - \frac{1}{2} (x - 2) + \frac{3}{8} (x - 2)^{2} - \frac{1}{4} (x - 2)^{3} + \frac{5}{32} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= \frac{1}{2} - \frac{1}{2} (x - 2) + \frac{3}{8} (x - 2)^{2} - \frac{1}{4} (x - 2)^{3} + \frac{5}{32} (x - 2)^{4} + \dots

\int \frac{x ^{2} - 18 x - 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

(x + y)^{2} d x + (2 x y + x^{2} - 1) d y = 0, y (1) = 1

\frac{\partial}{\partial y} (- sin (x y) x)

\frac{\partial}{\partial y} (5 x (4 + y)^{- 1})

5 y^{^{''}} - 6 y^{^{'}} + 5 y = 0

What is taylor 2/(x^2),2 ?
The answer to taylor 2/(x^2),2 is 1/2-1/2 (x-2)+3/8 (x-2)^2-1/4 (x-2)^3+5/32 (x-2)^4+\ldots