What is taylor x^3,3 ?

The answer to taylor x^3,3 is 27+27(x-3)+9(x-3)^2+(x-3)^3

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taylor x^3,3

taylor

x^{3}, 3

27 + 27 (x - 3) + 9 (x - 3)^{2} + (x - 3)^{3}

Solution steps

Apply the Taylor Formula

= 27 + \frac{\frac{d}{d x} ( x ^{3} ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{3} ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{3} ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= 27 + \frac{27}{1 !} (x - 3) + \frac{18}{2 !} (x - 3)^{2} + \frac{6}{3 !} (x - 3)^{3} + \frac{0}{4 !} (x - 3)^{4} + \frac{0}{5 !} (x - 3)^{5} + \frac{0}{6 !} (x - 3)^{6} + \frac{0}{7 !} (x - 3)^{7} + \frac{0}{8 !} (x - 3)^{8} + \frac{0}{9 !} (x - 3)^{9} + \frac{0}{10 !} (x - 3)^{10}

Refine

= 27 + 27 (x - 3) + 9 (x - 3)^{2} + (x - 3)^{3}

\int x^{10} e^{x^{11}} d x

\frac{d}{d x} (7 sin^{2} (x))

f (x) = 1 - 3 x, at x = - 1

\frac{d}{d x} (\frac{3 x ^{2} - 1}{x - 2})

f (x) = sec (x), at x = (\frac{π}{3})

What is taylor x^3,3 ?
The answer to taylor x^3,3 is 27+27(x-3)+9(x-3)^2+(x-3)^3