What is taylor x^{9/6} ?

The answer to taylor x^{9/6} is 1+3/2 (x-1)+3/8 (x-1)^2-1/16 (x-1)^3+3/128 (x-1)^4+\ldots

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taylor x^{9/6}

taylor

x^{\frac{9}{6}}

1 + \frac{3}{2} (x - 1) + \frac{3}{8} (x - 1)^{2} - \frac{1}{16} (x - 1)^{3} + \frac{3}{128} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{\frac{9}{6}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{9}{6}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{9}{6}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{3}{2}}{1 !} (x - 1) + \frac{\frac{3}{4}}{2 !} (x - 1)^{2} + \frac{- \frac{3}{8}}{3 !} (x - 1)^{3} + \frac{\frac{9}{16}}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + \frac{3}{2} (x - 1) + \frac{3}{8} (x - 1)^{2} - \frac{1}{16} (x - 1)^{3} + \frac{3}{128} (x - 1)^{4} + \dots

f (x) = - 10 x^{2} + 1760 x - 50000

f (t) = 9 t - 2 t^{2}

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{t} cos (t)

x \to 0 lim (\frac{1}{1 - x})

x \to 2 lim (5 x)

What is taylor x^{9/6} ?
The answer to taylor x^{9/6} is 1+3/2 (x-1)+3/8 (x-1)^2-1/16 (x-1)^3+3/128 (x-1)^4+\ldots