What is taylor (x-pi)^3 ?

The answer to taylor (x-pi)^3 is -pi^3+3pi^2x-3pix^2+x^3

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taylor (x-pi)^3

taylor

(x - π)^{3}

- π^{3} + 3 π^{2} x - 3 π x^{2} + x^{3}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= - π^{3} + 3 π^{2} x - 3 π x^{2} + x^{3}

n = 1 \sum \infty 3 n

\frac{d}{d x} (300 x (1 - x))

\int x csc (x) cot (x) d x

\int_{0}^{8} x + 1 d x

\int sec (2 x + 1) tan (2 x + 1) d x

What is taylor (x-pi)^3 ?
The answer to taylor (x-pi)^3 is -pi^3+3pi^2x-3pix^2+x^3