What is taylor 1/x ,2 ?

The answer to taylor 1/x ,2 is 1/2-1/4 (x-2)+1/8 (x-2)^2-1/16 (x-2)^3+1/32 (x-2)^4+\ldots

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taylor 1/x ,2

taylor

\frac{1}{x}, 2

\frac{1}{2} - \frac{1}{4} (x - 2) + \frac{1}{8} (x - 2)^{2} - \frac{1}{16} (x - 2)^{3} + \frac{1}{32} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= \frac{1}{2} - \frac{1}{4} (x - 2) + \frac{1}{8} (x - 2)^{2} - \frac{1}{16} (x - 2)^{3} + \frac{1}{32} (x - 2)^{4} + \dots

3 sin (- 2 x^{2})

x \to 0 lim ((1 + 2 x)^{\frac{1}{2 x ^{2}}})

\frac{d}{d x} (2 sin^{3} (x))

\int_{- 2}^{3} x^{2} - 4 d x

\int \frac{- 3}{y} d y

What is taylor 1/x ,2 ?
The answer to taylor 1/x ,2 is 1/2-1/4 (x-2)+1/8 (x-2)^2-1/16 (x-2)^3+1/32 (x-2)^4+\ldots