What is taylor x^{3/2} ?

The answer to taylor x^{3/2} 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^{3/2}

taylor

x^{\frac{3}{2}}

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

x \to 7 lim (2 - x - 3)

\int e^{x} 39 + e^{x} d x

f (x) = x^{3} + 3, (1, 2)

\int - 3 x d x

e^{3 t}

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