taylor 3/x

Solution

taylor

\frac{3}{x}

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 + \frac{- 3}{1 !} (x - 1) + \frac{6}{2 !} (x - 1)^{2} + \frac{- 18}{3 !} (x - 1)^{3} + \frac{72}{4 !} (x - 1)^{4} + \dots

Refine

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

\int \frac{x + 1}{x - 1} d x

\int \frac{( - x ^{2} - 1 )}{( x ^{2} - 1 )} d x

f (x) = arcsin (2 x)

\int_{0}^{1} 7 e^{- 4 x} d x

x \to 3 lim (lo g_{4} (3 x - 5))

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