What is taylor \sqrt[4]{x} ?

The answer to taylor \sqrt[4]{x} is 1+1/4 (x-1)-3/32 (x-1)^2+7/128 (x-1)^3-77/2048 (x-1)^4+\ldots

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taylor \sqrt[4]{x}

taylor

4 x

1 + \frac{1}{4} (x - 1) - \frac{3}{32} (x - 1)^{2} + \frac{7}{128} (x - 1)^{3} - \frac{77}{2048} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{4}}{1 !} (x - 1) + \frac{- \frac{3}{16}}{2 !} (x - 1)^{2} + \frac{\frac{21}{64}}{3 !} (x - 1)^{3} + \frac{- \frac{231}{256}}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + \frac{1}{4} (x - 1) - \frac{3}{32} (x - 1)^{2} + \frac{7}{128} (x - 1)^{3} - \frac{77}{2048} (x - 1)^{4} + \dots

\int 3 + s (s + 1)^{2} d s

f (x) = ln (25 sin^{2} (x))

y (X) = 0.167 X

(- 2, 4), (5, - 1)

x \to 0 lim (x^{9 s i n (x)})

What is taylor \sqrt[4]{x} ?
The answer to taylor \sqrt[4]{x} is 1+1/4 (x-1)-3/32 (x-1)^2+7/128 (x-1)^3-77/2048 (x-1)^4+\ldots