taylor 2/x

Solution

taylor

\frac{2}{x}

2 - 2 (x - 1) + 2 (x - 1)^{2} - 2 (x - 1)^{3} + 2 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{- 2}{1 !} (x - 1) + \frac{4}{2 !} (x - 1)^{2} + \frac{- 12}{3 !} (x - 1)^{3} + \frac{48}{4 !} (x - 1)^{4} + \dots

Refine

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

y^{^{''}} - a y = 0

\int_{1}^{2} x e^{- x^{2}} d x

(0, 0), (- 5, 3)

\int csc^{2} (\frac{x}{2}) d x

\frac{s + 5}{s ^{2} + 4 s + 3}

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