What is taylor (x+2)^{-1} ?

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

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taylor (x+2)^{-1}

taylor

(x + 2)^{- 1}

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

Solution steps

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( ( x + 2 ) ^{- 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x + 2 ) ^{- 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x + 2 ) ^{- 1} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

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

Refine

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

x \to - 1 - lim (1)

\frac{5}{t}

\frac{d}{d x} (\frac{2 x ^{3} + 4}{x ^{2} + 1})

\int \frac{cos ( x )}{2 + sin ( x )} d x

\int r (cos (θ)) z^{3}

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