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}

\int \frac{e ^{2 x}}{5 + e ^{x}} d x

f (x) = ln (x) - \frac{1}{x}

x^{3} (1 - x)^{100} + x^{4} - 5 π

\frac{d}{d x} (3 x^{3} - 64 x)

x \to 1 + lim (tan (\frac{π x}{2}))

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