What is taylor x^3,1 ?

The answer to taylor x^3,1 is 1+3(x-1)+3(x-1)^2+(x-1)^3

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taylor x^3,1

taylor

x^{3}, 1

1 + 3 (x - 1) + 3 (x - 1)^{2} + (x - 1)^{3}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{3}{1 !} (x - 1) + \frac{6}{2 !} (x - 1)^{2} + \frac{6}{3 !} (x - 1)^{3} + \frac{0}{4 !} (x - 1)^{4} + \frac{0}{5 !} (x - 1)^{5} + \frac{0}{6 !} (x - 1)^{6} + \frac{0}{7 !} (x - 1)^{7} + \frac{0}{8 !} (x - 1)^{8} + \frac{0}{9 !} (x - 1)^{9} + \frac{0}{10 !} (x - 1)^{10}

Refine

= 1 + 3 (x - 1) + 3 (x - 1)^{2} + (x - 1)^{3}

(1 + t^{2}) \frac{d y}{d t} + 4 t y = (1 + t^{2})^{- 2}

x \to \infty + lim (e^{x})

\int_{0}^{3} 0.2 e^{- 0.2 x} d x

\int 20 sin^{2} (x co) s^{2} x d x

\frac{d}{d x} (36 x^{\frac{1}{2}})