taylor x^3

Solution

taylor

x^{3}

x^{3}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{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

= x^{3}

n = 0 \sum \infty cos^{2} (n)

\frac{d}{d x} (\frac{x}{a} + \frac{a}{x})

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}})

\frac{d}{d y} (4 y^{3})

\int_{0}^{9} (2 x^{3} + 1) d x