What is taylor x^{5/7} ?

The answer to taylor x^{5/7} is 1+5/7 (x-1)-5/49 (x-1)^2+15/343 (x-1)^3-60/2401 (x-1)^4+\ldots

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taylor x^{5/7}

taylor

x^{\frac{5}{7}}

1 + \frac{5}{7} (x - 1) - \frac{5}{49} (x - 1)^{2} + \frac{15}{343} (x - 1)^{3} - \frac{60}{2401} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{\frac{5}{7}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{5}{7}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{5}{7}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{5}{7}}{1 !} (x - 1) + \frac{- \frac{10}{49}}{2 !} (x - 1)^{2} + \frac{\frac{90}{343}}{3 !} (x - 1)^{3} + \frac{- \frac{1440}{2401}}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + \frac{5}{7} (x - 1) - \frac{5}{49} (x - 1)^{2} + \frac{15}{343} (x - 1)^{3} - \frac{60}{2401} (x - 1)^{4} + \dots

f (x) = \frac{x + 9}{x - 9}

t^{2} y^{^{''}} - 5 t y^{^{'}} + 9 y = 0

x cos (3 x)

y^{^{'}} = x e^{y}, y (0) = 0

\frac{d}{d x} (arctan^{2} (\frac{1}{x}))

What is taylor x^{5/7} ?
The answer to taylor x^{5/7} is 1+5/7 (x-1)-5/49 (x-1)^2+15/343 (x-1)^3-60/2401 (x-1)^4+\ldots