What is taylor 5/x ,1 ?

The answer to taylor 5/x ,1 is 5-5(x-1)+5(x-1)^2-5(x-1)^3+5(x-1)^4+\ldots

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taylor 5/x ,1

taylor

\frac{5}{x}, 1

5 - 5 (x - 1) + 5 (x - 1)^{2} - 5 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 5 + \frac{\frac{d}{d x} ( \frac{5}{x} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{5}{x} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{5}{x} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 5 + \frac{- 5}{1 !} (x - 1) + \frac{10}{2 !} (x - 1)^{2} + \frac{- 30}{3 !} (x - 1)^{3} + \frac{120}{4 !} (x - 1)^{4} + \dots

Refine

= 5 - 5 (x - 1) + 5 (x - 1)^{2} - 5 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

\int_{2}^{7} \frac{1}{4 x + 8} d x

\int \frac{x + 1}{( x + 2 ) ( x - 3 )} d x

\int (tan (2 x) + cot (2 x))^{2} d x

\frac{6 x}{( 3 - 2 x ) ^{3}}

\frac{d}{d x} ((6 x + 5)^{2})

What is taylor 5/x ,1 ?
The answer to taylor 5/x ,1 is 5-5(x-1)+5(x-1)^2-5(x-1)^3+5(x-1)^4+\ldots