What is taylor sqrt(1+x^3) ?

The answer to taylor sqrt(1+x^3) is 1+1/2 x^3-1/8 x^6+\ldots

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taylor sqrt(1+x^3)

taylor

1 + x^{3}

1 + \frac{1}{2} x^{3} - \frac{1}{8} x^{6} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( 1 + x ^{3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 1 + x ^{3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 1 + x ^{3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 90}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \dots

Refine

= 1 + \frac{1}{2} x^{3} - \frac{1}{8} x^{6} + \dots

\frac{d}{d x} (e^{r (x) x})

\frac{d}{d y} (sin (x) cos (y))

f (x) = e^{- x^{2}}, at x = 5

x \to 0 lim (- \frac{3}{1 - 3 x})

f (x) = cot^{2} (sin (θ))

What is taylor sqrt(1+x^3) ?
The answer to taylor sqrt(1+x^3) is 1+1/2 x^3-1/8 x^6+\ldots