What is taylor x^{(1/3)} ?

The answer to taylor x^{(1/3)} is 1+1/3 (x-1)-1/9 (x-1)^2+5/81 (x-1)^3-10/243 (x-1)^4+\ldots

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taylor x^{(1/3)}

taylor

x^{(\frac{1}{3})}

1 + \frac{1}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{5}{81} (x - 1)^{3} - \frac{10}{243} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{3}}{1 !} (x - 1) + \frac{- \frac{2}{9}}{2 !} (x - 1)^{2} + \frac{\frac{10}{27}}{3 !} (x - 1)^{3} + \frac{- \frac{80}{81}}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + \frac{1}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{5}{81} (x - 1)^{3} - \frac{10}{243} (x - 1)^{4} + \dots

\int \frac{1}{1 - v ^{2}} d v

\frac{d}{d t} (1 - ∣ t ∣)

\int - sin (x) - e^{- x} + 3 x^{2} d x

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + e^{- x}

\frac{d y}{d x} = 2 x (y - 1)

What is taylor x^{(1/3)} ?
The answer to taylor x^{(1/3)} is 1+1/3 (x-1)-1/9 (x-1)^2+5/81 (x-1)^3-10/243 (x-1)^4+\ldots