What is taylor 4/(x+2),0 ?

The answer to taylor 4/(x+2),0 is 2-x+1/2 x^2-1/4 x^3+1/8 x^4+\ldots

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taylor 4/(x+2),0

taylor

\frac{4}{x + 2}, 0

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

Solution steps

Apply the Taylor Formula

= 2 + \frac{\frac{d}{d x} ( \frac{4}{x + 2} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{4}{x + 2} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{4}{x + 2} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

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

Refine

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

x \to \infty lim (10 \cdot e^{\frac{- x}{2}} + 4)

\frac{d y}{d x} = \frac{4 x}{9 y}

\frac{d}{d x} (e^{- 1 x})

(- 1, - 2), (3, 2)

ln (x + p)

What is taylor 4/(x+2),0 ?
The answer to taylor 4/(x+2),0 is 2-x+1/2 x^2-1/4 x^3+1/8 x^4+\ldots