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

t an g e n t \frac{6 x}{( 3 - 2 x ) ^{3}}

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

f (x) = - 3 x

t an g e n t x^{3} - 27 x

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