What is taylor 1/x ,x=2 ?

The answer to taylor 1/x ,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 ,x=2

taylor

\frac{1}{x}, 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

x \to - 6 + lim (\frac{- 9 x}{x + 6})

\int 2 y^{2} x - 3

\int e^{6 x} cos (7 x) d x

x \to 1 - lim (x^{2})

What is taylor 1/x ,x=2 ?
The answer to taylor 1/x ,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